The implicit partition algorithm used to solve fluid–structure coupling problems has high accuracy,but it requires a long computation time.In this paper,a semi-implicit fluid–structure coupling algorithm based on mo...The implicit partition algorithm used to solve fluid–structure coupling problems has high accuracy,but it requires a long computation time.In this paper,a semi-implicit fluid–structure coupling algorithm based on modal force prediction-correction is proposed to improve the computational efficiency.In the pre-processing stage,the fluid domain is assumed to be a pseudo-elastic solid and merged with the solid domain to form a holistic system,and the normalized modal information of the holistic system is calculated and stored.During the sub-step cycle,the modal superposition method is used to obtain the response of the holistic system with the predicted modal force as the load,so that the deformation of the structure and the updating of the fluid mesh can be achieved simultaneously.After solving the Reynolds-averaged Navier-Stokes equations in the fluid domain,the predicted modal force is corrected and a new sub-step cycle is started until the converged result is obtained.In this method,the computation of the fluid equations and the updating of the dynamic mesh are done implicitly,while the deformation of the structure is done explicitly.Two numerical cases,vortex induced oscillation of an elastic beam and fluid–structure interaction of a final stage blade,are used to verify the efficiency and accuracy of the proposed algorithm.The results show that the proposed method achieves the same accuracy as the implicit method while the computational time is reduced.In the case of the vortex-induced oscillation problem,the computational time can be reduced to 18.6%.In the case of the final stage blade vibration,the computational time can be reduced to 53.8%.展开更多
This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunzia...This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.展开更多
A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal d...A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal direction and z-level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohal Sea. The results are in good agreement both with the analytical solutions and measurement results.展开更多
A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 a...A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.展开更多
A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses parti...A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method （ICCG）, the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.展开更多
Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantit...Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.展开更多
In the case of a severe accident involving nuclear reactors,an important aspect that should be considered is the leakage of molten material from the inside of the reactor into the environment.These molten materials da...In the case of a severe accident involving nuclear reactors,an important aspect that should be considered is the leakage of molten material from the inside of the reactor into the environment.These molten materials damage other reactor components,such as electrical tubes,grid plates and core catchers.In this study,the moving particle semi-implicit(MPS)method is adopted and improved to analyze the twodimensional downward relocation process of molten Wood’s metal as a representation of molten material in a nuclear reactor.The molten material impinges the Wood’s metal plate(WMP),which is mounted on a rigid dummy stainless steel in a cylindrical test vessel.The breaching process occurs because of heat transfer between the molten material and WMP.The formed breach areas were in good agreement with the experimental results,and they showed that the molten Wood’s metal spread above the WMP.The solid WMP fraction decreased with time until it reached the termination time of the simulation.The present results show that the MPS method can be applied to simulate and analyze the downward relocation process of molten material in the grid plate of a nuclear reactor.展开更多
Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian g...Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.展开更多
In this paper,we present the semi-implicit Euler（SIE）numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square...In this paper,we present the semi-implicit Euler（SIE）numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.展开更多
A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) ...A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.展开更多
We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equati...We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation （image selective smoothing model） given by Alvarez et al. （Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29： 845-866）. Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W1＇2 （W1＇1） sense in isotropic （anisotropic） diffu- sion domain.展开更多
Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numer...Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.展开更多
The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all ...The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.展开更多
We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not...We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not possible.As shown in Boscarino et al.(J.Sci.Comput.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative solvers.In this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)methods.Our findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.展开更多
A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.Th...A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.展开更多
The aim of this paper is to give an appropriate numerical method to solve Allen-Cahn equation, with Dirichlet or Neumann boundary condition. The time discretization involves an explicit scheme for the nonlinear part o...The aim of this paper is to give an appropriate numerical method to solve Allen-Cahn equation, with Dirichlet or Neumann boundary condition. The time discretization involves an explicit scheme for the nonlinear part of the operator and an implicit Euler discretization of the linear part. Finite difference schemes are used for the spatial part. This finally leads to the numerical solution of a sparse linear system that can be solved efficiently.展开更多
In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to so...In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.展开更多
The definition of a reference state close to the realistic atmosphere in an atmospheric model is essential for deriving prognostic deviations and improving numerical accuracy.In this study,a new dynamical framework al...The definition of a reference state close to the realistic atmosphere in an atmospheric model is essential for deriving prognostic deviations and improving numerical accuracy.In this study,a new dynamical framework allowing easy switching between a one-dimensional(1D)and a three-dimensional(3D)time-independent reference state is developed for the semi-implicit semi-Lagrangian solver in a global non-hydrostatic atmospheric model on Yin–Yang grids.The 3D reference state is introduced with consideration of additional horizontal gradient terms of referencestate terms,which is different from the 1D reference state.It is characterized by reduced magnitude of deviations,more accurate pressure gradient force,as well as alleviated numerical noise.Four idealized benchmark tests and multiple full-physics real-case forecasts are carried out to assess the impact of the 3D and 1D reference states.The 3D reference state shows significant advantages in the simulation of atmospheric transport and wave propagation in the idealized experiments.In the real-case forecasts,batched forecasts from June to August 2021 show a comprehensive improvement in medium-range prediction by using the 3D reference state.The new scheme achieves an enhanced prediction skill for large-scale circulation and extends the effective forecast period by 0.8 days in the Northern Hemisphere.展开更多
The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer...The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer simulation methods are method of characteristics(MOC),and further investigation of new algorithms is needed.Therefore,a new method for simulating the water hammer using the finite volume method(FVM),semi-implicit method for pressure linked equations(SIMPLE)algorithm is proposed in the present work.Compared with the experimental data,the accuracy and reliability of the proposed algorithm are verified.Results show that the IAB,MIAB friction models not only predict the first pressure peak but also accurately predict the pressure attenuation.From the comparison of the MOC,SIMPLE algorithms,the results of the two algorithms are almost the same in front of the valve,while near the upstream tank,when using the same friction model,the pressure attenuation predicted by the SIMPLE algorithm is slightly greater than that of the MOC method and closer to the experimental data.Therefore,the newly proposed algorithm can serve as an alternative to the MOC method in simulating water hammer.The investigation enriches the numerical methods of hydraulic transients and lays the foundation for subsequent program development.展开更多
基金support of the National Natural Science Foundation of China(No.51675406)the Basic Research Project Group,China(No.514010106-205)。
文摘The implicit partition algorithm used to solve fluid–structure coupling problems has high accuracy,but it requires a long computation time.In this paper,a semi-implicit fluid–structure coupling algorithm based on modal force prediction-correction is proposed to improve the computational efficiency.In the pre-processing stage,the fluid domain is assumed to be a pseudo-elastic solid and merged with the solid domain to form a holistic system,and the normalized modal information of the holistic system is calculated and stored.During the sub-step cycle,the modal superposition method is used to obtain the response of the holistic system with the predicted modal force as the load,so that the deformation of the structure and the updating of the fluid mesh can be achieved simultaneously.After solving the Reynolds-averaged Navier-Stokes equations in the fluid domain,the predicted modal force is corrected and a new sub-step cycle is started until the converged result is obtained.In this method,the computation of the fluid equations and the updating of the dynamic mesh are done implicitly,while the deformation of the structure is done explicitly.Two numerical cases,vortex induced oscillation of an elastic beam and fluid–structure interaction of a final stage blade,are used to verify the efficiency and accuracy of the proposed algorithm.The results show that the proposed method achieves the same accuracy as the implicit method while the computational time is reduced.In the case of the vortex-induced oscillation problem,the computational time can be reduced to 18.6%.In the case of the final stage blade vibration,the computational time can be reduced to 53.8%.
基金funded by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2027 attributed to DICAM of the University of Trento(grant L.232/2016)in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications,the PRIN 2022 project High order structure-preserving semi-implicit schemes for hyperbolic equations.D.is member of INdAM GNCS and was also co-funded by the European Union NextGenerationEU(PNRR,Spoke 7 CN HPC).Views and opinions expressed are however those of the author(s)only and do not necessarily reflect those of the European Union or the European Research Council.Neither the European Union nor the granting authority can be held responsible for them.
文摘This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.
基金The Major State Basic Research Program of China under contract No. 2012CB417002the National Natural Science Foundation of China under contract Nos 50909065 and 51109039
文摘A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal direction and z-level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohal Sea. The results are in good agreement both with the analytical solutions and measurement results.
基金the National Natural Science Foundation of China (Grant No.50579035)
文摘A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.
基金the National Natural Science Foundation under Grant No.50579035
文摘A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method （ICCG）, the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.
文摘Semi-implicit direct kinetics(SIDK)is an innovative method for the temporal discretization of neutronic equations proposed by J.Banfield.The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations.Hence,these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained,which leads to a significant reduction in computational cost.As the fission source is not known in a time step,the original study suggested using a constant quantity pertaining to the previous time step for this purpose,and a reduction in the size of the time step was proposed to lessen the imposed errors.However,this remedy notably diminishes the main advantage of the SIDK method.We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications,the mentioned drawbacks will be mitigated adequately.To test this idea,a novel multigroup,multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states.In addition to the SIDK,two other kinetic methods,i.e.,direct kinetics and higher-order backward discretization,are programmed into the diffusion code for comparison with the proposed model.The final code is tested at different conditions of two well-known transient benchmark problems.Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods,it reduces the total time required for computation by up to 24%.
基金supported by the Pendidikan Magister Menuju Doktor untuk Sarjana Unggul(PMDSU)a research program from the Ministry of Research,Technology and Higher Education,IndonesiaThe authors wish to thank Prof.S.Koshizuka,Prof.M.Sakai and Dr.K.Shibata of the University of Tokyo for their helpful comments and for providing the basic MPS code for fluids。
文摘In the case of a severe accident involving nuclear reactors,an important aspect that should be considered is the leakage of molten material from the inside of the reactor into the environment.These molten materials damage other reactor components,such as electrical tubes,grid plates and core catchers.In this study,the moving particle semi-implicit(MPS)method is adopted and improved to analyze the twodimensional downward relocation process of molten Wood’s metal as a representation of molten material in a nuclear reactor.The molten material impinges the Wood’s metal plate(WMP),which is mounted on a rigid dummy stainless steel in a cylindrical test vessel.The breaching process occurs because of heat transfer between the molten material and WMP.The formed breach areas were in good agreement with the experimental results,and they showed that the molten Wood’s metal spread above the WMP.The solid WMP fraction decreased with time until it reached the termination time of the simulation.The present results show that the MPS method can be applied to simulate and analyze the downward relocation process of molten material in the grid plate of a nuclear reactor.
文摘Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.
基金Supported by the NSF of the Higher Education Institutions of Jiangsu Province(10KJD110006)Supported by the grant of Jiangsu Institute of Education(Jsjy2009zd03)Supported by the Qing Lan Project of Jiangsu Province(2010)
文摘In this paper,we present the semi-implicit Euler（SIE）numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.
基金Project supported by the National Natural Science Foundation of China (No.51078230)the Research Fund for the Doctoral Program of Higher Education of China (No.200802480056)the Key Project of Fund of Science and Technology Development of Shanghai (No.10JC1407900),China
文摘A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.
文摘We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation （image selective smoothing model） given by Alvarez et al. （Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29： 845-866）. Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W1＇2 （W1＇1） sense in isotropic （anisotropic） diffu- sion domain.
基金the National Natural Science Foundation of China(Nos.50979059 and 11272213)
文摘Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.
文摘The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.
基金Open Access funding provided by Universita degli Studi di Verona.
文摘We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not possible.As shown in Boscarino et al.(J.Sci.Comput.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative solvers.In this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)methods.Our findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.
基金funded by the research project STiMulUs,ERC Grant agreement no.278267Financial support has also been provided by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2022 attributed to DICAM of the University of Trento(Grant L.232/2016)the PRIN2017 project.The authors have also received funding from the University of Trento via the Strategic Initiative Modeling and Simulation.
文摘A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.
文摘The aim of this paper is to give an appropriate numerical method to solve Allen-Cahn equation, with Dirichlet or Neumann boundary condition. The time discretization involves an explicit scheme for the nonlinear part of the operator and an implicit Euler discretization of the linear part. Finite difference schemes are used for the spatial part. This finally leads to the numerical solution of a sparse linear system that can be solved efficiently.
基金the European Union’s NextGenerationUE-Project:Centro Nazionale HPC,Big Data e Quantum Computing,“Spoke 1”(No.CUP E63C22001000006)E.Macca was partially supported by GNCS No.CUP E53C22001930001 Research Project“Metodi numericiper problemi differenziali multiscala:schemi di alto ordine,ottimizzazione,controllo”+1 种基金E.Macca and S.Boscarino would like to thank the Italian Ministry of Instruction,University and Research(MIUR)to supportthis research with funds coming from PRIN Project 2022(2022KA3JBA,entitled“Advanced numericalmethods for time dependent parametric partial differential equations and applications”)Sebastiano Boscarinohas been supported for this work from Italian Ministerial grant PRIN 2022 PNRR“FIN4GEO:forward andinverse numerical modeling of hydrothermalsystemsin volcanic regions with application to geothermal energyexploitation”(No.P2022BNB97).E.Macca and S.Boscarino are members of the INdAM Research groupGNCS.
文摘In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.
基金Supported by the National Natural Science Foundation of China(42375153,42075151,and 42205157).
文摘The definition of a reference state close to the realistic atmosphere in an atmospheric model is essential for deriving prognostic deviations and improving numerical accuracy.In this study,a new dynamical framework allowing easy switching between a one-dimensional(1D)and a three-dimensional(3D)time-independent reference state is developed for the semi-implicit semi-Lagrangian solver in a global non-hydrostatic atmospheric model on Yin–Yang grids.The 3D reference state is introduced with consideration of additional horizontal gradient terms of referencestate terms,which is different from the 1D reference state.It is characterized by reduced magnitude of deviations,more accurate pressure gradient force,as well as alleviated numerical noise.Four idealized benchmark tests and multiple full-physics real-case forecasts are carried out to assess the impact of the 3D and 1D reference states.The 3D reference state shows significant advantages in the simulation of atmospheric transport and wave propagation in the idealized experiments.In the real-case forecasts,batched forecasts from June to August 2021 show a comprehensive improvement in medium-range prediction by using the 3D reference state.The new scheme achieves an enhanced prediction skill for large-scale circulation and extends the effective forecast period by 0.8 days in the Northern Hemisphere.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52079140,52379095)。
文摘The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer simulation methods are method of characteristics(MOC),and further investigation of new algorithms is needed.Therefore,a new method for simulating the water hammer using the finite volume method(FVM),semi-implicit method for pressure linked equations(SIMPLE)algorithm is proposed in the present work.Compared with the experimental data,the accuracy and reliability of the proposed algorithm are verified.Results show that the IAB,MIAB friction models not only predict the first pressure peak but also accurately predict the pressure attenuation.From the comparison of the MOC,SIMPLE algorithms,the results of the two algorithms are almost the same in front of the valve,while near the upstream tank,when using the same friction model,the pressure attenuation predicted by the SIMPLE algorithm is slightly greater than that of the MOC method and closer to the experimental data.Therefore,the newly proposed algorithm can serve as an alternative to the MOC method in simulating water hammer.The investigation enriches the numerical methods of hydraulic transients and lays the foundation for subsequent program development.
