径向基函数及移动网格在Euler方程数值计算中的应用

基于二维Euler方程,在利用弹簧技术的移动非结构三角形网格上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三角形单元构造插值径向基函数,而在计算交界面的流通量采用两点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。

Radial Basis Functions and Moving Meshes with Applications to Numerical Calculations of Euler Equations

An ENO finite volume method which is constructed on the basis of radial basis functions on moving unstructured triangular meshes by spring principium is introduced.In order to obtain the higher accuracy on spatial discretization,an interpolation radial basis function is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on every edge of every triangular 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.