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

Vincenzo Gulizzi, Vincenzo Gulizzi, John B. Bell, Ann S. Almgren

Risultato della ricerca: Articlepeer review

6 Citazioni (Scopus)


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.
Lingua originaleEnglish
pagine (da-a)110861-
Numero di pagine26
RivistaJournal of Computational Physics
Stato di pubblicazionePublished - 2022

All Science Journal Classification (ASJC) codes

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  • ???subjectarea.asjc.3100.3101???
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  • ???subjectarea.asjc.1700.1706???
  • ???subjectarea.asjc.2600.2605???
  • ???subjectarea.asjc.2600.2604???
  • ???subjectarea.asjc.2600.2612???


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