一种求解Euler方程的新型高阶精度数值方法  

A Novel High-Order Numerical Method for Solving Euler Equations

作　　者：陈烨[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2014年第4期622-631,共10页Chinese Quarterly of Mechanics

摘　　要：提出了一种求解Euler方程的新型高阶精度数值方法.该数值方法基于一种新的矢通量分裂格式,将矢通量项分裂成压力通量项和对流通量项.与传统矢通量分裂格式相比,新的矢通量分裂格式能够更好地捕捉特征场内的中间特征波,从而增强格式的分辨率.同时,为了提高这种矢通量分裂格式的空间精度,我们在近似求解压力通量项黎曼问题时对界面处的独立物理变量进行高阶插值.在时间步上,采用显式最优的三阶龙格-库塔方法进行推进.数值试验表明,与传统数值方法相比,本文提出的新方法同时具有高精度和高分辨率的优点.A novel nttmerical method was developed for solving Euler equations. The principal strategy of this method was to combine a first-order flux-vector splitting scheme characterized by accurate resolution of intermediate characteristic fields and a fourth-order compact MUSCL TVD interpolation reconstruction step of primitive flow variables at interface for the generalized Riemann problem. The optimal three-order Runge-Kutta method was employed in time integration. Through some benchmark test problems for Euler equations in both one and two spatial dimensions, this novel numerical method demonstrated both high-order accuracy and high resolution.

关 键 词：EULER方程 直接数值模拟 有限差分法 矢通量分裂 高分辨率 

分 类 号：O354[理学—流体力学]