Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows

TL;DR

This paper presents a space-time adaptive ADER-DG finite element method with a posteriori sub-cell WENO limiting for simulating non-stationary compressible multicomponent reactive flows, effectively handling stiff reactions and detonation wave propagation.

Contribution

The paper introduces a novel combined space-time adaptive ADER-DG method with a posteriori sub-cell WENO limiting for complex reactive flow simulations, avoiding splitting and fractional step methods.

Findings

Successfully simulated ZND detonation wave propagation.

Demonstrated effectiveness in handling stiff reaction problems.

Achieved accurate results without directional splitting.

Abstract

The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to simulate non-stationary compressible multicomponent reactive flows. The multicomponent composition of the reacting medium and the reactions occurring in it were described by expanding the original system of Euler equations by a system of non-stationary convection-reaction equations. The use of this method to simulate high stiff problems associated with reactions occurring in a multicomponent medium requires the use of the adaptive change in the time step. The solution of the classical problem related to the formation and propagation of a ZND detonation wave is carried out. It was shown that the space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter can be used to simulate flows without using of splitting in directions and fractional step methods.