hp-Adaptive Finite Element Simulations of Viscous Flow Including Convective Heat Transfer

Abstract

An hp-adaptive finite element model based on mesh refinement and increasing spectral order is used to solve for viscous flow problems including natural and forced convection. The adaptive FEM produces highly accurate numerical results. An a-posteriori error estimator based on the L ₂ norm is employed to guide the adaptive procedure. Example problems include lid-driven cavity viscous flow, natural convection in a differentially heated square enclosure and forced convection over a backward facing step. Results compared with data reported in the literature show excellent agreement.