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 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 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
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 simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrins...A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrinsic partial differentialequation for updating the position vector of evolving family of plane curves. A curvecan be evolved in the normal direction by a combination of fourth order terms relatedto the intrinsic Laplacian of the curvature, second order terms related to the curva-ture, first order terms related to anisotropy and by a given external velocity field. Theevolution is numerically stabilized by an asymptotically uniform tangential redistri-bution of grid points yielding the first order intrinsic advective terms in the governingsystem of equations. By using a semi-implicit in time discretization it can be numer-ically approximated by a solution to linear penta-diagonal systems of equations (inpresence of the fourth order terms) or tri-diagonal systems (in the case of the secondorder terms). Various numerical experiments of plane curve evolutions, including, inparticular, nonlinear, anisotropic and regularized backward curvature flows, surfacediffusion and Willmore flows, are presented and discussed.展开更多
In this paper,we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations.Stabilized semi-implicit schemes are used for temporal discretization,a...In this paper,we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations.Stabilized semi-implicit schemes are used for temporal discretization,and the finite element method is used for spatial discretization.It is shown that by adding a single linear term that is of the same order with the truncation error in time,the proposed methods are all unconditionally energy stable.Error estimates for the two schemes are also established.Numerical examples are presented to confirm the accuracy,efficiency and stability of the proposed methods.展开更多
Transcritical film cooling was investigated by numerical study in a methane cooled methane/oxygen rocket engine.The respective time-averaged Navier-Stokes equations have been solved for the compressible steady three-d...Transcritical film cooling was investigated by numerical study in a methane cooled methane/oxygen rocket engine.The respective time-averaged Navier-Stokes equations have been solved for the compressible steady three-dimensional(3-D) flow.The flow field computations were performed using the semi-implicit method for pressure linked equation(SIMPLE) algorithm on several blocks of nonuniform collocated grid.The calculation was conducted over a pressure range of 202 650.0 Pa to 1.2×107 Pa and a temperature range of 120.0 K to 3 568.0 K.Twenty-nine different cases were simulated to calculate the impact of different factors.The results show that mass flow rate,length,diameter,number and diffused or convergence of film jet channel,injection angle and jet array arrangements have great impact on transcritical film cooling effectiveness.Furthermore,shape of the jet holes and jet and crossflow turbulence also affect the wall temperature distribution.Two rows of film arranged in different axial angles and staggered arrangement were proposed as new liquid film arrangement.Different radial angles have impact on the film cooling effectiveness in two row-jets cooled cases.The case of in-line and staggered arrangement are almost the same in the region before the second row of jets,but a staggered arrangement has a higher film cooling effectiveness from the second row of jets.展开更多
In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attach...In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation （SIMPLE） algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.展开更多
A numerical simulation method for parachute Fluid-Structure Interaction （FSI） problem using Semi-Implicit Method for Pres- sure-Linked Equations （SIMPLE） algorithm is proposed. This method could be used in both co...A numerical simulation method for parachute Fluid-Structure Interaction （FSI） problem using Semi-Implicit Method for Pres- sure-Linked Equations （SIMPLE） algorithm is proposed. This method could be used in both coupling computation of para- chute FSI and flow field analysis. Both fiat circular parachute and conical parachute are modeled and simulated by this new method. Flow field characteristics at various angles of attack are further simulated for the conical parachute model. Compari- son with the space-time FSI technique shows that this method also provides similar and reasonable results.展开更多
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.
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.
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This work was supported by grants:VEGA 1/0269/09,APVV-0351-07,APVV-RPEU-0004-07(K.Mikula and M.Balazovjech)and APVV-0247-06(D.Sevcovic).
文摘A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrinsic partial differentialequation for updating the position vector of evolving family of plane curves. A curvecan be evolved in the normal direction by a combination of fourth order terms relatedto the intrinsic Laplacian of the curvature, second order terms related to the curva-ture, first order terms related to anisotropy and by a given external velocity field. Theevolution is numerically stabilized by an asymptotically uniform tangential redistri-bution of grid points yielding the first order intrinsic advective terms in the governingsystem of equations. By using a semi-implicit in time discretization it can be numer-ically approximated by a solution to linear penta-diagonal systems of equations (inpresence of the fourth order terms) or tri-diagonal systems (in the case of the secondorder terms). Various numerical experiments of plane curve evolutions, including, inparticular, nonlinear, anisotropic and regularized backward curvature flows, surfacediffusion and Willmore flows, are presented and discussed.
基金supported by Department of Education of Hunan Province Project(No.22C0491)Zhou’s research was supported by key project of Hunan Education Department(No.23A0143)National Key Research and Development Program of China(No.2023YFA1009100).
文摘In this paper,we consider two stabilized second-order semi-implicit finite element methods for solving the Allen-Cahn and Cahn-Hilliard equations.Stabilized semi-implicit schemes are used for temporal discretization,and the finite element method is used for spatial discretization.It is shown that by adding a single linear term that is of the same order with the truncation error in time,the proposed methods are all unconditionally energy stable.Error estimates for the two schemes are also established.Numerical examples are presented to confirm the accuracy,efficiency and stability of the proposed methods.
文摘Transcritical film cooling was investigated by numerical study in a methane cooled methane/oxygen rocket engine.The respective time-averaged Navier-Stokes equations have been solved for the compressible steady three-dimensional(3-D) flow.The flow field computations were performed using the semi-implicit method for pressure linked equation(SIMPLE) algorithm on several blocks of nonuniform collocated grid.The calculation was conducted over a pressure range of 202 650.0 Pa to 1.2×107 Pa and a temperature range of 120.0 K to 3 568.0 K.Twenty-nine different cases were simulated to calculate the impact of different factors.The results show that mass flow rate,length,diameter,number and diffused or convergence of film jet channel,injection angle and jet array arrangements have great impact on transcritical film cooling effectiveness.Furthermore,shape of the jet holes and jet and crossflow turbulence also affect the wall temperature distribution.Two rows of film arranged in different axial angles and staggered arrangement were proposed as new liquid film arrangement.Different radial angles have impact on the film cooling effectiveness in two row-jets cooled cases.The case of in-line and staggered arrangement are almost the same in the region before the second row of jets,but a staggered arrangement has a higher film cooling effectiveness from the second row of jets.
文摘In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation （SIMPLE） algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.
基金supported by the National Natural Science Foundation of China (Grant No. 10577003)Monash University of Australia
文摘A numerical simulation method for parachute Fluid-Structure Interaction （FSI） problem using Semi-Implicit Method for Pres- sure-Linked Equations （SIMPLE） algorithm is proposed. This method could be used in both coupling computation of para- chute FSI and flow field analysis. Both fiat circular parachute and conical parachute are modeled and simulated by this new method. Flow field characteristics at various angles of attack are further simulated for the conical parachute model. Compari- son with the space-time FSI technique shows that this method also provides similar and reasonable results.
