一维Euler方程的高分辨率有限体积格式
A High Resolution Finite Volume Scheme forOne Dimensional Euler Equations

作者: 康亦欣 , 高 巍 :内蒙古大学数学科学学院,内蒙古 呼和浩特; 谢桃枫 :内蒙古医科大学计算机信息学院,内蒙古 呼和浩特;

关键词: Euler方程Hermite插值高阶格式CBCTVDEuler Equations Hermite Interpolation High Resolution CBC TVD

摘要:
本文提出一种高精度有限体积格式数值求解一维Euler方程。为克服线性高阶格式在解的间断附近产生非物理振荡,作者利用Hermite插值多项式,结合对流有界性准则TVD和CBC构造了本文的数值格式。典型算例验证表明,本数值格式可以很好的计算一维Euler方程的间断初值问题。

Abstract: In this paper, a high resolution finite volume scheme is proposed to solve one dimensional Euler equations. We use the Hermite interpolation method to construct the present scheme. Two kinds of convection boundedness criteria TVD and CBC are combined to suppress nonphysical wiggles of linear schemes near discontinuities. Some typical test cases show that the present numerical scheme can solve one dimensional Euler equation with discontinuous initial profiles efficiently.

文章引用: 康亦欣 , 谢桃枫 , 高 巍 (2017) 一维Euler方程的高分辨率有限体积格式。 流体动力学, 5, 56-68. doi: 10.12677/IJFD.2017.52007

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