A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp...

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Vydáno v:Journal of computational physics Ročník 450; s. 110861
Hlavní autoři: Gulizzi, Vincenzo, Almgren, Ann S., Bell, John B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge Elsevier Inc 01.02.2022
Elsevier Science Ltd
Témata:
Accuracy
Algorithms
Basis functions
Cartesian coordinates
Computational physics
Discontinuity
Discontinuous Galerkin methods
Domains
Embedded boundaries
Exact solutions
Finite volume method
Finite Volume methods
Galerkin method
Gas dynamics
Grid refinement (mathematics)
hp-AMR
Ideal gas
Quadratures
Runge-Kutta method
Shock-capturing schemes
Structured grids (mathematics)
Discontinuous Galerkin methods
Shock-capturing schemes
Embedded boundaries
hp-AMR
Finite Volume methods
ISSN:0021-9991, 1090-2716
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Shrnutí:We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities. •Two- and three-dimensional embedded geometries are resolved with high-order accuracy.•Discontinuous Galerkin (dG) methods provide high-order accuracy in regions of smooth flow.•A Finite Volume (FV) method provides robust shock-tracking capabilities of solution discontinuities.•An hp adaptive mesh refinement strategy enables the coupling between dG schemes and the FV scheme.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110861