A composite grid solver for conjugate heat transfer in fluid–structure systems

We describe a numerical method for modeling temperature-dependent uid ow coupled to heat transfer in solids. This approach to conjugate-heat-transfer can be used to compute transient and steady-state solutions to a wide range of uid-solid systems in complex two- and three-dimensional geometry. Fluids are modeled with the temperature dependent incompressible Navier-Stokes equations using the Boussinesq approximation. Solids with heat transfer are modeled with the heat equation. Appropriate interface equations are applied to couple the solutions across dierent domains. The computational region is divided into a number of sub-domains corresponding to uid domains and solid domains. There may be multiple uid domains and multiple solid domains. Each uid or solid sub-domain is discretized with an overlapping grid. The entire region is associated with a composite grid which is the union of the overlapping grids for the sub-domains. A dierent physics solver ( uid solver or solid solver) is associated with each sub-domain. A higher-level multi-domain solver manages the entire solution process. We propose and analyze some centered discrete approximations to the interface equations that have some desirable stability properties. The coupled interface equations may be solved directly when using explicit time-stepping meth-ods in the sub-domains, resulting in a strongly coupled approach. The stability of the interface treatment in this case is independent of the relative sizes of the material properties in the two domains with the time-step only dependin