A high-order discontinuous Galerkin discretization with multiwavelet-based grid adaptation for compressible flows. (English) Zbl 1462.65141
Summary: Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin discretization can be performed using multiwavelets, which allow for higher-order vanishing moments, while maintaining local support. An implementation for scalar one-dimensional conservation laws has already been developed and tested. In the present paper we extend this strategy to systems of equations, in particular to the equations governing inviscid compressible flow.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65T60 | Numerical methods for wavelets |
| 76N06 | Compressible Navier-Stokes equations |
| 35Q31 | Euler equations |
Keywords:
grid adaptivity; multiresolution analysis; high-order methods; multiwavelet; discontinuous Galerkin; conservation lawsSoftware:
HE-E1GODFReferences:
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