三维非结构网格上求解双曲型守恒律方程的一类三阶精度有限体积格式  

A THIRD ORDER FINITE VOLUME SCHEME FOR SOLVING 3D HYPERBOLIC CONSERVATION LAWS ON UNSTRUCTURED TETRAHEDRAL MESHES

作　　者：唐玲艳[1] 傅浩[1] 宋松和[1] 

机构地区：[1]国防科学技术大学理学院数学与系统科学系,长沙410073

出　　处：《数值计算与计算机应用》2013年第3期212-220,共9页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11001027;10971226;61171018;91130013);中国博士后科学基金资助项目

摘　　要：考虑标量双曲型守恒律方程,对三维非结构四面体网格给出了一类满足局部极值原理的三阶精度有限体积格式.方法的主要思想是时间和空间分开处理,时间离散采用三阶TVD RungeKutta方法;对空间,在每一个四面体单元上基于最小二乘原理构造一个二次多项式,结合数值解光滑探测器和梯度限制器,使其在光滑区域具有高阶精度,在间断区域满足局部极值原理.该格式具有间断分辨能力高,编程实现简便,计算速度快等优点.典型算例的数值试验表明,该格式是有效的.This paper introduces a third order accuracy finite volume scheme that satisfies the local maximum principle for solving three-dimensional hyperbolic conservation laws on unstruc- tured tetrahedral meshes. The main idea is to separate temporal and spatial diseretization. The temporal derivatives are discretized by the third order TVD R.unge-Kutta method. For spatial discretization, a quadratic polynomial is constructed on every tetrahedral mesh based on the least square principle. Combined with the smoothness indicator and gradient limiter, the scheme can obtain high-order accuracy in the smooth region and satisfy the local max- imum principle near singularities. The new scheme has the advantages of good resolution of singularities, programming easily and fast computational speed. Typical numerical tests demonstrate its efficiency.

关 键 词：双曲型守恒律方程 非结构四面体网格 高精度方法 

分 类 号：O241.8[理学—计算数学]