We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of plana...We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.展开更多
MAGIC is one of the most widely used models for forecasting long-term acidification. The model's code, however, has been experiencing numerical instability, though this might not be widely known to the public user...MAGIC is one of the most widely used models for forecasting long-term acidification. The model's code, however, has been experiencing numerical instability, though this might not be widely known to the public users. The major instability comes from the analytical solution to two cubic equations for calculating SO42- concentration and the exchangeable fraction of Al on the soils. The mathematical algorithm for calculating the concentration of SO42- from a quadratic equation is also found instable. This paper is aimed at improving the instability above through proved numerical algorithms.展开更多
The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with t...The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with the cosmic background）. The dispersion relation that does not consider magnetic fields is described by the well- known Buneman relation. In 2011, Bohata, Bren and Kulhanek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches ωn（k） is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accom- panied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet - intergalactic medium in- teraction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.展开更多
The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the probl...The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.展开更多
In this note,we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations.The idea of this method is to combine a”full-wave”Riemann solve...In this note,we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations.The idea of this method is to combine a”full-wave”Riemann solver and a”less-wave”Riemann solver,which uses a special modified weight based on the difference in velocity vectors.It is also found that such blending does not need to be implemented in all equations of the Euler system.We point out that the proposed method is easily extended to other”full-wave”fluxes that suffer from shock instability.Some benchmark problems are presented to validate the proposed method.展开更多
In order to expand the study on flow instability of supercritical circulating fluidized bed(CFB) boiler,a new numerical computational model considering the heat storage of the tube wall metal was presented in this pap...In order to expand the study on flow instability of supercritical circulating fluidized bed(CFB) boiler,a new numerical computational model considering the heat storage of the tube wall metal was presented in this paper.The lumped parameter method was proposed for wall temperature calculation and the single channel model was adopted for the analysis of flow instability.Based on the time-domain method,a new numerical computational program suitable for the analysis of flow instability in the water wall of supercritical CFB boiler with annular furnace was established.To verify the code,calculation results were respectively compared with data of commercial software.According to the comparisons,the new code was proved to be reasonable and accurate for practical engineering application in analysis of flow instability.Based on the new program,the flow instability of supercritical CFB boiler with annular furnace was simulated by time-domain method.When 1.2 times heat load disturbance was applied on the loop,results showed that the inlet flow rate,outlet flow rate and wall temperature fluctuated with time eventually remained at constant values,suggesting that the hydrodynamic flow was stable.The results also showed that in the case of considering the heat storage,the flow in the water wall is easier to return to stable state than without considering heat storage.展开更多
This paper improves the discrete vortex method for modeling Kelvin-Helmholtz instability and Rayleigh-Tay- lor instability by proper choice of velocity weighted average coefficients, redistribution of markers and succ...This paper improves the discrete vortex method for modeling Kelvin-Helmholtz instability and Rayleigh-Tay- lor instability by proper choice of velocity weighted average coefficients, redistribution of markers and successive adding of computational points with the increase of interfacial deformation and gives the numerical results of Rayleigh-Taylor instability. The numerical results show that the first two techniques greatly enhance the ability of the discrete vortex method for modeling large interracial deformations and the last technique greatly reduces the computational amounts of the numerical modeling at large deformation stage. The numerical modeling of Rayleigh- Taylor instability not only reproduces some phenomena such as the roll up at the end part of the spike observed in experiments but also finds some new phenomena such as the splashes at the roll up parts which needs to be tested by experiment.展开更多
The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods.The hybrid method of combining high resolution flux with more dissipative solver is an attractive attemp...The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods.The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon.In this paper,a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes.By combining the Roe with HLL flux in different directions and different flux components,we give an interesting explanation to the linear numerical instability.Based on such analysis,some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability.Numerical experiments are presented to verify our analysis results.The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.展开更多
The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid.For some applications,such as modeling biological materials,capturing internal boundary v...The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid.For some applications,such as modeling biological materials,capturing internal boundary viscosity is important.We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow.We find that the explicit time immersed boundary update is unconditionally unstable above a critical boundary to fluid viscosity ratio for a Kelvin-Voigt material.We also show there is a severe time step restriction when simulating a standard linear boundary with a small relaxation time scale using the same explicit update.A stable implicit method is presented to overcome these computation challenges.展开更多
We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis o...We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。
文摘We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.
文摘MAGIC is one of the most widely used models for forecasting long-term acidification. The model's code, however, has been experiencing numerical instability, though this might not be widely known to the public users. The major instability comes from the analytical solution to two cubic equations for calculating SO42- concentration and the exchangeable fraction of Al on the soils. The mathematical algorithm for calculating the concentration of SO42- from a quadratic equation is also found instable. This paper is aimed at improving the instability above through proved numerical algorithms.
基金supported by the Czech Technical University in Prague with grants SGS10/266/OHK3/3T/13 (Electric discharges, basic research and application,SGS12/181/OHK3/3T/13 (Plasma instabilities and plasma-particle interactions)by the Grant Agency of the Czech Republic with grant GD205/09/H033 (General relativity and its applications in astrophysics and cosmology)
文摘The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with the cosmic background）. The dispersion relation that does not consider magnetic fields is described by the well- known Buneman relation. In 2011, Bohata, Bren and Kulhanek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches ωn（k） is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accom- panied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet - intergalactic medium in- teraction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.
基金funding from the European Community’s Seventh Framework Program (FP7/2007-2013) under grant agreement 225967 ‘‘Next Mu SE”supported by the National Natural Science Foundation of China (Nos. 11202013, 11572025 and 51420105008)
文摘The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.
基金supported in part by the National Natural Science Foundation of China under(Grant No.10871029)foundation of LCP.
文摘In this note,we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations.The idea of this method is to combine a”full-wave”Riemann solver and a”less-wave”Riemann solver,which uses a special modified weight based on the difference in velocity vectors.It is also found that such blending does not need to be implemented in all equations of the Euler system.We point out that the proposed method is easily extended to other”full-wave”fluxes that suffer from shock instability.Some benchmark problems are presented to validate the proposed method.
基金supported by the "Strategic Priority Research Program" of the Chinese Academy of Sciences,Grant No.XDA07030100the National Key Technology R&D Program of China during the 12th Five-Year Plan Period No.2015BAA03B01-01
文摘In order to expand the study on flow instability of supercritical circulating fluidized bed(CFB) boiler,a new numerical computational model considering the heat storage of the tube wall metal was presented in this paper.The lumped parameter method was proposed for wall temperature calculation and the single channel model was adopted for the analysis of flow instability.Based on the time-domain method,a new numerical computational program suitable for the analysis of flow instability in the water wall of supercritical CFB boiler with annular furnace was established.To verify the code,calculation results were respectively compared with data of commercial software.According to the comparisons,the new code was proved to be reasonable and accurate for practical engineering application in analysis of flow instability.Based on the new program,the flow instability of supercritical CFB boiler with annular furnace was simulated by time-domain method.When 1.2 times heat load disturbance was applied on the loop,results showed that the inlet flow rate,outlet flow rate and wall temperature fluctuated with time eventually remained at constant values,suggesting that the hydrodynamic flow was stable.The results also showed that in the case of considering the heat storage,the flow in the water wall is easier to return to stable state than without considering heat storage.
文摘This paper improves the discrete vortex method for modeling Kelvin-Helmholtz instability and Rayleigh-Tay- lor instability by proper choice of velocity weighted average coefficients, redistribution of markers and successive adding of computational points with the increase of interfacial deformation and gives the numerical results of Rayleigh-Taylor instability. The numerical results show that the first two techniques greatly enhance the ability of the discrete vortex method for modeling large interracial deformations and the last technique greatly reduces the computational amounts of the numerical modeling at large deformation stage. The numerical modeling of Rayleigh- Taylor instability not only reproduces some phenomena such as the roll up at the end part of the spike observed in experiments but also finds some new phenomena such as the splashes at the roll up parts which needs to be tested by experiment.
基金supported by the National Natural Science Foundation of China(11071025)the Foundation of CAEP(2010A0202010)the Foundation of National Key Laboratory of Science and Technology Computation Physics and the Defense Industrial Technology Development Program(B1520110011).
文摘The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods.The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon.In this paper,a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes.By combining the Roe with HLL flux in different directions and different flux components,we give an interesting explanation to the linear numerical instability.Based on such analysis,some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability.Numerical experiments are presented to verify our analysis results.The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.
基金supported in part by the NIH Glue Grant‘Cell Migration Consortium’(NIGMS U54 GM64346)to Alex Mogilner as well as by NSF-DMS grant 0540779 and UCOP grant 09-LR-03-116724-GUYR to RG.
文摘The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid.For some applications,such as modeling biological materials,capturing internal boundary viscosity is important.We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow.We find that the explicit time immersed boundary update is unconditionally unstable above a critical boundary to fluid viscosity ratio for a Kelvin-Voigt material.We also show there is a severe time step restriction when simulating a standard linear boundary with a small relaxation time scale using the same explicit update.A stable implicit method is presented to overcome these computation challenges.
基金This work was supported by the National Natural Science Foundation of China(No.11472004)the Foundation of Innovation of NUDT(No.B150106).
文摘We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.
