一种求解Euler方程的简化气体动理学模型

摘要

基于一种简化的平衡分布函数，提出一种新的动理学通量矢量分裂（ Kinetic Flux Vector Splitting ，KFVS）格式来求解Euler方程。算例证实，新的KFVS格式继承了原始KFVS格式中捕捉激波准确、无数值震荡的优点。与原始的KFVS格式相比，由于简化的平衡分布函数与Maxwellian平衡分布函数相比复杂程度大大降低，计算中不需要再计算误差函数，新的KFVS格式的计算效率得到了很大提高。在同样的计算精度下，新KFVS格式比原始KFVS格式计算效率提高了一倍以上，显示了新格式具有良好的数值模拟性能。%Based on a simplified equilibrium distribution function , a new Kinetic Flux Vector Splitting ( KFVS) scheme is proposed for solving Euler equations .It is proved in two cases that the new scheme in-herits the some advantages of original KFVS scheme ,which are accuracy in shock capture and non-oscil-lation after shock wave .Besides,the calculation efficiency is greatly improved by the new KFVS scheme due to its simple equilibrium distribution function compared with Maxwellian equilibrium distribution function in the original one and consequently the error function ,a very time-consuming process in the o-riginal KFVS ,is not needed in the flux calculation .So it is not surprising that new KFVS scheme only takes about half time to complete the same simulation on the same degree of accurate compared with the original KFVS,which shows its good performance in numerical simulation .