Adaptive multiresolution computations applied to detonations

TL;DR

This paper introduces a space-time adaptive finite volume method with multiresolution analysis for reactive Euler equations, effectively capturing detonation phenomena in 1D and 2D with improved efficiency.

Contribution

It presents a novel adaptive multiresolution approach combined with explicit time splitting for reactive gas flow simulations, enhancing accuracy and computational efficiency.

Findings

Adaptive scheme achieves comparable accuracy to regular grid methods.

Significant reduction in CPU time and memory usage.

Effective handling of stiff reactive problems with explicit methods.

Abstract

A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and dynamic space adaptivity is introduced using multiresolution analysis. A time splitting method of Strang is applied to be able to consider stiff problems while keeping the method explicit. For time adaptivity an improved Runge--Kutta--Fehlberg scheme is used. Applications deal with detonation problems in one and two space dimensions. A comparison of the adaptive scheme with reference computations on a regular grid allow to assess the accuracy and the computational efficiency, in terms of CPU time and memory requirements.