A numerical method for simulation of forced convection in a composite porous/fluid system

A new unstructured-grid high-order characteristics upwind finite-volume algorithm for accurate numerical simulation of incompressible laminar flow and forced convection heat transfer over a composite system containing simultaneously porous-saturated region and fluid region is presented in this paper. It is an upwind method at both the differential equation and discretized equation levels based on the method of characteristics. Flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristics speed. In addition, an upwind-based interpolation method of third-order accuracy is used for interpolating flow variables on an unstructured grid. With these inherent upwind techniques for evaluation of convection fluxes at control volume surfaces, no artificial viscosity is required. The discretized equations are then solved by an explicit multistage Runge-Kutta time stepping scheme together with a point-implicit treatment of the source terms. Unified governing equations for the fluid and porous media regions are employed, and the matching conditions at the fluid-porous interface are thus satisfied automatically. This significantly reduces the complexity of the traditional method, which considers two regions separately. A detailed numerical investigation of fluid flow over a backward-facing step with a porous block insert directly behind the step is performed, in order to validate the numerical method, demonstrate the accuracy and robustness of the scheme proposed and explore the use of porous inserts for heat transfer enhancement in recirculating flow.