A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avo...A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.展开更多
使用激波捕捉法求解以数学间断作为初始条件的无黏可压缩流场时,间断结构会逐渐演变为包含多个网格节点的数值过渡区,在此过程中会产生两个平行于间断且规则分布的非物理波动。使用捕捉法计算激波流场时,流场参数应满足修正方程,但作为...使用激波捕捉法求解以数学间断作为初始条件的无黏可压缩流场时,间断结构会逐渐演变为包含多个网格节点的数值过渡区,在此过程中会产生两个平行于间断且规则分布的非物理波动。使用捕捉法计算激波流场时,流场参数应满足修正方程,但作为初始条件进行计算的初始激波满足Euler方程,两者之间的矛盾是产生初始激波诱导非物理波动的原因。鉴于激波等间断是由特征型Euler方程定义的,从该方程出发构造了一种基于特征值迎风特性的通量计算格式(upwind flux scheme based on characteristics,UFSC),并采用若干种常规守恒型通量分裂格式作为参考。数值计算结果表明,UFSC可以消除Steger-Warming、Van Leer等矢通量分裂格式的初始接触间断诱导非物理波动,还可以减小初始激波诱导扰动的幅值。在光滑流场区域,UFSC和矢通量分裂格式的计算结果相近,但是在强激波附近会出现较大的压力尖峰。为克服这一缺陷,进一步构造了在激波区域和其他区域分别采用Steger-Warming格式和UFSC格式计算的混合通量计算格式UFSC+S,可以有效抑制初始激波诱导误差,提高计算精度。展开更多
基金Supported by the National Basic Research Program of China(2012CB825601)the National Natural Science Foundationof China(41031066,41231068,41274192,41074121,41204127)+1 种基金the Knowledge Innovation Program of the ChineseAcademy of Sciences(KZZD-EW-01-4)the Specialized Research Fund for State Key Laboratories
文摘A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.
文摘使用激波捕捉法求解以数学间断作为初始条件的无黏可压缩流场时,间断结构会逐渐演变为包含多个网格节点的数值过渡区,在此过程中会产生两个平行于间断且规则分布的非物理波动。使用捕捉法计算激波流场时,流场参数应满足修正方程,但作为初始条件进行计算的初始激波满足Euler方程,两者之间的矛盾是产生初始激波诱导非物理波动的原因。鉴于激波等间断是由特征型Euler方程定义的,从该方程出发构造了一种基于特征值迎风特性的通量计算格式(upwind flux scheme based on characteristics,UFSC),并采用若干种常规守恒型通量分裂格式作为参考。数值计算结果表明,UFSC可以消除Steger-Warming、Van Leer等矢通量分裂格式的初始接触间断诱导非物理波动,还可以减小初始激波诱导扰动的幅值。在光滑流场区域,UFSC和矢通量分裂格式的计算结果相近,但是在强激波附近会出现较大的压力尖峰。为克服这一缺陷,进一步构造了在激波区域和其他区域分别采用Steger-Warming格式和UFSC格式计算的混合通量计算格式UFSC+S,可以有效抑制初始激波诱导误差,提高计算精度。
