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

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.

arXiv comment20 pages, 11 figures, 2 tables

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Cited by in corpus (5)

• Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation
• High order well-balanced Arbitrary-Lagrangian-Eulerian ADER discontinuous Galerkin schemes on general polygonal moving meshes
• Arbitrary high order ADER-DG method with local DG predictor for solutions of initial value problems for systems of first-order ordinary differential equations
• High order ADER-DG method with local DG predictor for solutions of differential-algebraic systems of equations
• Improving the local solution of the DG predictor of the ADER-DG method for solving systems of ordinary differential equations and its applicability to systems of differential-algebraic equations