Automatic grid refinement and higher order flux discretization for diffusion modeling

Modern numerical process simulators are becoming increasingly complicated in both physical models and domain shape. Grid generation is difficult for these simulators because of the inherent transient nature of the problems being solved. This paper addresses adaptive grid refinement for use in solving diffusion problems. It additionally investigates higher order approximations to the discretized diffusion flux. Several methods of both adaptive grid refinement and discretization are investigated and compared in terms of CPU time and final discretization error. All the methods are directly applied to the one-dimensional version of SUPREM-IV.