AN ADAPTIVE GRID SOLUTION PROCEDURE FOR CONVECTION DIFFUSION-PROBLEMS

A computationally efficient and stable adaptive grid solution procedure is developed for convection diffusion problems. In this method, grid refinement and adaptation is based on an equidistribution law but is only performed in regions with high error estimates that are flagged from a preliminary coarse grid solution. The equidistribution law is implicit in the grid generation procedure which requires the solution of two Poisson equations with control functions that are obtained directly from the error estimates or weighting functions at the grid points. Solution on the refined, equidistributed mesh in the flagged region is obtained with boundary conditions interpolated from the coarse grid results. Accurate solutions in both the flagged region and the coarse grid regions of the domain are obtained with a multigrid approach that requires successive solutions on the refined, equidistributed mesh in the flagged region and on the coarse mesh in the entire domain. The adaptive grid method including the multigrid calculations can be extended to several levels of refinement. The acronym LAME is coined for this procedure in view of its Local Adaptation, Multigridding, and Equidistribution features. The method is shown to be stable, computationally efficient, and accurate by applying it to three test problems and comparing with conventional calculations on a fixed curvilinear grid. © 1990.