A filtering monotonization approach for DG discretizations of hyperbolic problems

Abstract

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the $deal.II$ numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique.

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• A Posteriori Subcell Limiting of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws
• Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
• Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemes
• An efficient filtered scheme for some first order Hamilton-Jacobi-Bellman equations

Cited by in corpus (3)

• An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases
• Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning
• A quantitative comparison of high-order asymptotic-preserving and asymptotically-accurate IMEX methods for the Euler equations with non-ideal gases