h-Adaptivity and "honest" GFEM for advection-dominated transport

A standard two-dimensional Galerkin finite-element method (GFEM) code for coupled Navier-Stokes and energy equations is used with h-adaptive meshing based on a posteriori error estimation using the superconvergent patch recovery technique for solving a range of advection-dominated transport problems. It is demonstrated that such a method provides a highly effective, simple, and efficient way of dealing with the perennial problems in numerical modeling of advection-dominated transport, such as oscillations or wiggles with central difference-type discretizations (such as GFEM) and numerical ("false") diffusion when wiggle-suppressant schemes are used. Additionally, the auto-adaptive finite-element method provides a powerful means of achieving optimal solutions without having to pre-define a mesh, which may be either inadequate or too expensive. A number of benchmark problems are presented as application examples for this method before solving a problem of natural convection in an air-filled cavity with various orientations, for which experimental results are available.