Automatic grid refinement and higher order flux discretization for diffusion modeling

The authors point out that 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 inherently transient nature of the problems being solved. Here, adaptive grid refinement is considered for use in solving diffusion problems. Higher order approximations to the discretized diffusion flux are also studied. 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