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
The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to ...The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed,and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust.More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.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
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 this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylin...In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.展开更多
A hybrid numerical flux scheme is proposed by adapting the carbunclefree modified Harten-Lax-van Leer contact(HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact(HLLC) scheme in regions of shear. This ...A hybrid numerical flux scheme is proposed by adapting the carbunclefree modified Harten-Lax-van Leer contact(HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact(HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.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.
基金Project supported by the National Natural Science Foundation of China(Nos.51736008 and 51276092)
文摘The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed,and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust.More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.
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 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The project supported by the National Natural Science Foundation of China (10176033, 10135010 and 90205025)The English text was polished by Yunming Chen
文摘In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.
基金the Singapore Ministry of Education AcRF Tier-2 Grant(No.MOE2014-T2-1-002)the Graduate Research Officer Scholarship from School of Mechanical and Aerospace Engineering,Nanyang Technological University,Singapore。
文摘A hybrid numerical flux scheme is proposed by adapting the carbunclefree modified Harten-Lax-van Leer contact(HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact(HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.
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.
