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

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

doi:10.1016/j.jcp.2021.110861

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

Journal Article · Mon Nov 22 23:00:00 EST 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110861· OSTI ID:1815406

^[1]; Almgren, Ann S. ^[1]; Bell, John B. ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Herein, 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1815406

Alternate ID(s):: OSTI ID: 1833882
OSTI ID: 1923891

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 450; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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