An Adaptive Simplex Cut-Cell Method for High-Order Discontinuous Galerkin Discretizations of Conjugate Heat Transfer Problems

Abstract

In this paper we present a PDE solution framework for high-order discretizations of conjugate heat transfer (CHT) problems on non-body-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an anisotropic output-based adaptive scheme. With the cut-cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the DG discretization automatically adjusts the mesh in each sub-domain and achieves high-order accuracy in outputs of interest, namely heat flux across an interface. We demonstrate our proposed framework through several multi-domained CHT problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be di cult to capture with user generated meshes. Our proposed automatic mesh generation and adaptation scheme o↵ers a hands-free capability allowing for streamlined solutions and physical insight to complex CHT problems.

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

“…On the other side, high-order of convergence methods (of at least third-order) are becoming more popular as the demand for more efficient and accurate computer simulations increases as a result of more-than-ever complex engineering problems. 34,35 High-order of convergence methods for conjugate heat transfer problems are found in the context of the internal penalty discontinuous Galerkin method, 36,37 hybridizable discontinuous Galerkin method, [38][39][40][41] cut-cell discontinuous Galerkin method, 42,43 weak Galerkin finite element method, 44,45 finite element method, [46][47][48][49][50][51][52] finite difference method, [53][54][55][56][57] finite cell method, 58 among others. Although these promising techniques succeed in providing approximate solutions with higher accuracy and lower computational cost, when compared with the second-order accurate methods, many numerical aspects have to be taken into account.…”

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

“…However, when generating cut meshes for n ‐regioned domains, junction points, which join multiple regions (e.g., point A in Figure ), are encountered, warranting additional region information to precisely define the topology of the cut mesh. The intersection algorithm is briefly described in this section, and more details can be found in Ojeda .…”