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

We describe a numerical method for modeling temperature-dependent fluid flow 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 fluid-solid systems in complex twoand 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 different domains. The computational region is divided into a number of sub-domains corresponding to fluid domains and solid domains. There may be multiple fluid domains and multiple solid domains. Each fluid 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 different physics solver (fluid 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 methods 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 depending on the usual von Neumann conditions for each sub-domain. For implicit time-stepping methods we solve the interface equations in a weakly-coupled fashion to avoid forming a coupled implicit system across all sub-domains. The convergence of this approach does depend on the relative sizes of the thermal conductivities and diffusivities. We analyze different iteration strategies for solving these implicit equations including the use of mixed (Robin) approximations at the interface. Numerical results are presented to illustrate the method. The accuracy of the technique is verified using the method of analytic solutions and by computing the solution to some heat exchanger problems where the exact solution is known. The technique is also applied to the modeling of an inertial-confinement-fusion hohlraum target and the flow of coolant past an hexagonal array of heated fuel rods. The multi-domain solver runs in parallel on distributed memory computers and some parallel results are provided.