An internal penalty discontinuous Galerkin method for simulating conjugate heat transfer in a closed cavity

Abstract

Summary Using the discontinuous Galerkin (DG) method for conjugate heat transfer problems can provide improved accuracy close to the fluid‐solid interface, localizing the data exchange process, which may further enhance the convergence and stability of the entire computation. This paper presents a framework for the simulation of conjugate heat transfer problems using DG methods on unstructured grids. Based on an existing DG solver for the incompressible Navier‐Stokes equation, the fluid advection‐diffusion equation, Boussinesq term, and solid heat equation are introduced using an explicit DG formulation. A Dirichlet‐Neumann partitioning strategy has been implemented to achieve the data exchange process via the numerical flux of interface quadrature points in the fluid‐solid interface. Formal h and p convergence studies employing the method of manufactured solutions demonstrate that the expected order of accuracy is achieved. The algorithm is then further validated against 3 existing benchmark cases, including a thermally driven cavity, conjugate thermally driven cavity, and a thermally driven cavity with conducting solid, at Rayleigh numbers from 1000 to 100 000. The computational effort is documented in detail demonstrating clearly that, for all cases, the highest‐order accurate algorithm has several magnitudes lower error than first‐ or second‐order schemes for a given computational effort.

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.…”

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

“…For the purpose of remaining consistent with the meshes and boundary conditions, the strength of the thermal interaction is controlled by either varying the solid conductivity λ s , or by varying the order of the polynomial approximation P . Increasing P alters the cell proportion where the nearest Gauss point is located χ, and thus alters the calculation of the amplification factor and Biot number as shown in equations (20) and (22). This has an interesting consequence in which a configuration that would have a weak fluidstructure interaction with polynomial approximation P = 1 may have a moderate interaction with P = 2.…”

“…The use of DG methods for CHT processes has been a recent development. Cai and Thornber demonstrated improved accuracy on a CHT problem using the incompressible Navier-Stokes equations with the Boussinesq approximation [22]. Hao et al used a Dirichlet-Neumann coupling procedure to show improvements in precision using DG solvers when compared to CHT processes using a second-order FD fluid solver [23], [24].…”