A High-order Discontinuous Galerkin Method for Simulating Incompressible Fluid-Thermal-Structural Problems

Abstract

The use of discontinuous Galerkin (DG) methods to solve fluid thermal structure interaction problems in numerical modelling is known to offer several advantages. In particular, DG methods provide the flexibility of using different approximations in different elements, which makes the methods ideal for hp-adaptivity. The first objective of this thesis is to present a framework for the computation of fluid thermal structure interaction problems within both the single and multi-solid domain using DG methods on unstructured grids. The full solver consists of four main components: the incompressible fluid solver, the conjugate heat transfer solver, the linear elastic solver and the fluid to structure interaction solver. Based on an earlier developed DG solver for the incompressible Navier-Stokes equation, the fluid advection-diffusion equation, the Boussinesq term, the solid heat equation and the linear elastic 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. Computational effort is documented in detail demonstrating precisely that for all cases the highest order accurate algorithm has several magnitudes lower error than lower-order schemes for a given computational effort. Secondly, this thesis has proposed a detailed compact thermoelectric cooler (TEC) modelling method based on an existing black box like compact TEC model. Close comparisons validate that both the detailed and the black box like compact model are accurate enough to simulate the conduction only case. When air convection is required to carry out a system-level thermal management optimization, the detailed compact modelling method is more reliable.