A GENERAL BOUNDARY CONDITION TREATMENT IN IMMERSED BOUNDARY METHODS FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH HEAT TRANSFER

A general boundary condition scheme for incompressible flows over immersed bodies on Cartesian grids is developed to treat Dirichlet, Neumann, and Robin boundary conditions on the immersed surfaces. Various forced and natural convection problems over a circular cylinder and the nature convection between two concentric cylinders are computed to validate the proposed scheme. Results show that the method is second-order in L-1 and L-2 norms for velocity, pressure, and temperature for all three boundary conditions. The method is also second-order in L-infinity norm for Dirichlet boundary condition, while it is of the order of 1.4 in L-infinity norm when Neumann or Robin condition is applied.