Local time-stepping for adaptive multiresolution using natural extension of Runge–Kutta methods - Archive ouverte HAL
Article Dans Une Revue Journal of Computational Physics Année : 2019

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

Résumé

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.
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Dates et versions

hal-02616166 , version 1 (05-04-2024)

Identifiants

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Muller Moreira Lopes, Margarete Oliveira Domingues, Kai Schneider, Odim Mendes. Local time-stepping for adaptive multiresolution using natural extension of Runge–Kutta methods. Journal of Computational Physics, 2019, 382, pp.291-318. ⟨10.1016/j.jcp.2018.10.052⟩. ⟨hal-02616166⟩
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