High-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

被引：18

作者：

Nazari, Farshid ^{[1
]}

Mohammadian, Abdolmajid ^{[1
]}

Charron, Martin ^{[2
]}

机构：

[1] Univ Ottawa, Dept Civil Engn, Ottawa, ON K1N 6N5, Canada

[2] Environm Canada, Atmospher Numer Weather Predict Res Div, Haliburton, ON, Canada

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 286卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Low-dissipation low-dispersion; Optimal schemes; High-order accurate; Nonlinear advection; Computational acoustics; Diagonally-implicit; Time integration; Runge-Kutta; ATMOSPHERIC BOUNDARY-LAYER; FINITE-DIFFERENCE SCHEMES; COMPUTATIONAL ACOUSTICS;

D O I：

10.1016/j.jcp.2015.01.020

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

High-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes are analyzed and introduced, based on the optimization of amplification and phase errors for wave propagation. Various optimized schemes can be obtained. The new scheme shows negligible dissipation. It is illustrated mathematically and numerically that the new scheme preserves fourth-order accuracy, while the recently developed diagonally implicit Runge-Kutta scheme does not. The numerical applications contain the advection equation with and without a stiff nonlinear source term and an oscillatory test. The new scheme is A-stable as desired for the solution of stiff problems. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：38 / 48

页数：11

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