Local time-stepping for adaptive multiresolution using natural extension of Runge-Kutta methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:382

Article

Lopes, Muller Moreira^1,4  Domingues, Margarete Oliveira^2,4  Schneider, Kai⁵  Mendes, Odim^3,4 

[1] Grad Program Appl Comp CAP, Sao Jose Dos Campos, Brazil

[2] Coordinat Associated Labs CTE, Associate Lab Appl Comp & Math LAC, Sao Jose Dos Campos, Brazil

[3] Coordinat Space Sci CEA, Space Geophys Div DGE, Sao Jose Dos Campos, Brazil

[4] Natl Inst Space Res INPE, Av Astronautas 1758, BR-12227010 Sao Jose Dos Campos, SP, Brazil

[5] Aix Marseille Univ, Inst Math Marseille, CNRS, Cent Marseille, 39 Rue F Joliot Curie, F-13453 Marseille 13, France

关键词: Multiresolution analysis;    Finite volume;    Local time-stepping;    Runge-Kutta;   

DOI  :  10.1016/j.jcp.2018.10.052

来源: Elsevier

【 摘 要 】

A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes, endowed with cell average multiresolution analysis for triggering the dynamical grid adaptation. The explicit time scheme features a natural extension of Runge-Kutta methods which allow local time-stepping while guaranteeing accuracy. The use of a compact Runge-Kutta formulation permits further memory reduction. The precision and computational efficiency of the scheme regarding CPU time and memory compression are assessed for problems in one, two and three space dimensions. As application Burgers equation, reaction-diffusion equations and the compressible Euler equations are considered. The numerical results illustrate the efficiency and superiority of the proposed local time-stepping method with respect to the reference computations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free