The moving discontinuous Galerkin method with interface condition enforcement for the simulation of hypersonic, viscous flows

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient fl...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2024-07, Vol.427, p.117045, Article 117045
Main Authors: Ching, Eric J., Kercher, Andrew D., Corrigan, Andrew
Format: Article
Language:English
Subjects:
Anisotropic curvilinear r-adaptivity
Discontinuous Galerkin method
Implicit shock fitting
Interface condition enforcement
MDG-ICE
Mesh adaptation
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Summary:The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg–Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent element degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that reduces grid motion in directions with small element length scales, an element shape regularization that mitigates excessive element curvature, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2024.117045