A Study of the Effect of Higher Order Spatial Discretizations in SAMR (Structured Adaptive Mesh Refi

Generally, adaptively refined meshes aim to concentrate grid points in regions of interest while leaving the bulk of the domain sparsely meshed, thus reducing the computational time. Structured adaptively refined meshes in particular overlay grids of different refinement until the required accuracy is achieved. If the depth of the grid hierarchy is an issue (e.g. computational overheads) and has to be kept below a certain maximum, higher accuracy can be achieved either by increasing the mesh refinement factor or by using higher order spatial discretizations and interpolants. In this study, we present our findings for various orders of spatial discretizations as applied to two SAMR simulations: one for the FitzHughNagumo equation and the other for a -Air reaction-diffusion system. We investigate in detail the pairing of the orders of the spatial discretizations and the interpolants and their effect on the overall order of accuracy. We also demonstrate that higher-order SAMR approaches can be computationally more economical compared to second-order approaches.