An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with...

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Bibliographic Details
Published in:Journal of computational physics 2014-12, Vol.278, p.445-468
Main Authors: Sun, Huafei, Darmofal, David L.
Format: Article
Language:English
Subjects:
Adaptation
Conjugate heat transfer
Conjugates
Continuity
Convergence
Cut cells
Discontinuous Galerkin
Discretization
Galerkin methods
Heat transfer
High-order method
Interface problems
Mathematical models
Strategy
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Summary:In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.08.035