A diffuse interface immersed boundary method for convective heat and fluid flow

Abstract

The immersed boundary method is extended to a diffuse solid–fluid interface alleviating the need of reconstruction near a solid wall. The scope of a solid surface, felt through a non zero volume fraction, is limited within one grid cell. The no-slip condition is realized in the limit of sufficiently finer mesh. A single universal equation is approximated in the entire domain using geometrically constructed volume fraction. A predictor–corrector type of time marching algorithm is used to solve the conservation equations where variables are defined in non-staggered arrangement. Second order approximation of volume integrals results in linear systems that are only a weak function of the object geometry. A Heaviside function based triangulation of the interfacial cells is found to produce highly accurate volume fractions. The computed data shows second order convergence with grid spacing while linearized body resolution does not have appreciable effect on the solution. The method is tested in problems that involve three modes of convective heat transfer with single/multiple, stationary/dynamic objects. Comparison with reported data reveals the accuracy, versatility and promise of the method for heat transfer on complex geometries.