A new class of diagonally implicit Runge-Kutta methods with zero dissipation and minimized dispersion error

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:376

Article

Giri, Subhajit¹  Sen, Shuvam¹ 

[1] Tezpur Univ, Dept Math Sci, Tezpur 784028, Assam, India

关键词: Time integration;    Diagonally implicit;    Runge-Kutta;    Wave propagation;    Low-dissipation low-dispersion;    Computational acoustics;   

DOI  :  10.1016/j.cam.2020.112841

来源: Elsevier

【 摘 要 】

In this work, we propose a new class of A-stable diagonally implicit four stage Runge-Kutta (R-K) methods with minimal dissipation and optimally low dispersion error. These schemes obtained by minimizing both amplification and phase error enjoy fourth order of accuracy and are suitable for stiff systems. Emphasis here is to outline an algorithm that can be used to develop diagonally implicit R-K methods of diverse stages having low-dissipation low-dispersion virtues while retaining, to a large extent, inherent stability and high accuracy. This algorithm is subsequently applied to propose two, three and four stage diagonally implicit R-K schemes. One and two dimensional, linear and non-linear propagation problems are numerically tackled at a relatively higher CFL number and a comprehensive comparison is carried out with other stable diagonally implicit schemes available in the literature to exhibit benefits of optimization. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free