Abstract
This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced character of the resulting numerical method for smooth stationary solutions. The strategy can be adapted to some well-known different time marching DG discretisations. Particularly, in this article, Runge–Kutta DG and ADER DG methods are studied. Additionally, a limiting procedure based on a modified WENO approach is described to deal with the spurious oscillations generated in the presence of non-smooth solutions, keeping the well-balanced properties of the scheme intact. The resulting numerical method is then exactly well-balanced and high-order in space and time for smooth solutions. Finally, some numerical results are depicted using different systems of balance laws to show the performance of the introduced numerical strategy.
Highlights
This paper extends the numerical strategy introduced within the framework of finite volume methods in [35] to Discontinuous Galerkin (DG) methods, describing a general approach to preserve stationary solutions for general systems of conservation laws
We propose a spatial DG discretization method that exactly preserves stationary solutions
We have presented a novel and general technique for preserving stationary solutions for Discontinuous Galerkin methods
Summary
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