Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part II. High-Order Conjugate Heat Transfer (Advances in Applied Mathematics and Mechanics, 2025)
A high-order unified solution method is presented for simulating the coupled fluid flow and heat transfer phenomena in solid materials. The method integrates the energy transfer processes of fluid and solid by transforming the compressible Navier-Stokes equations into a dimensionless system through a double-time-scaleapproach. A time scaling factor is introduced into the system to bridge and expeditethe energy transfer processes between the mediums, thereby accelerating convergencetowards a global steady state. To ensure consistent accuracy across material interfaces,high-order formulations are introduced to obtain the interface temperature and heatflux. The effectiveness of the methods are verified and validated through numericalexperiments with a three-dimensional discontinuous Galerkin flow solver. Numericalresults demonstrate the globally high-order accuracy of the unified method for fluid-solid conjugate heat transfer problems, enabling rapid and robust convergence withlarge CFL numbers of up to $10^8.$