径向基函数在三维Euler方程数值计算中的应用

摘要

基于三维Euler方程,对非结构四面体网格给出了一种基于紧支径向基函数重构的ENO型有限体积格式,方法的主要思想是先对每一个四面体单元构造插值径向基函数,而在计算交界面的流通量采用高斯积分公式以保证格式的整体精度,时间离散采用三阶TVD Runge-Kutta方法.最后用该格式对一些典型算例进行了数值模拟,结果表明该方法计算速度快,对间断有很好的分辨能力.%An ENO finite volume method which is constructed on the basis of radial basis functions onunstructured tetrahedral meshes is introduced. In order to obtain the higher accuracy on spatial discretization, an interpolation radial basis function is constructed on every tetrahedral mesh. Gauss quadrature formula is also used on every edge of every tetrahedral mesh and the third order TVD Runge-Kutta method is used for time discretization. Numerical experiments show that the method compute fast and improve resolving power of the discontinuous domain.