A parallel multilevel method for adaptively refined Cartesian grids with embedded boundaries

. Asrecently as five to ten years ago, mesh generation was fre-quently the most time consuming task in a typical CFD cycle.Adaptive Cartesian mesh generation methods are capable ofproducing millions of cells around complex geometries inminutes and have substantially removed this bottleneck.Why write yet another Euler solver? With robust mesh gener-ation largely in-hand, solution time resurfaces as the pacingitem in the CFD cycle. The current work attacks this issue bydesigning a scalable, accurate Cartesian solver with robustmultigrid convergence acceleration. Our primary motivationis to gain efficiency by capitalizing on the simplifications andspecialized data structures available on Cartesian grids. Sig-nificant savings in both CPU time and storage may be real-ized by taking advantage of the fact that cell faces arecoordinate aligned. In addition, higher-order methods withgood limiters are generally easier to design and perform morerobustly on uniform Cartesian meshes.Secondly, in any embedded-boundary Cartesian solver, thebody-intersectingcut-cellsdemand special attention. Thesecells can impose a substantial burden on the numerical dis-cretization since the arbitrary nature of geometric intersec-tion implies that a cut-cell may be orders of magnitudesmaller than its neighboring cells. This fact contrasts sharplywith the comparatively smooth meshes that are generallyfound on a good quality structured or unstructured mesh.Substantial research into these cut-cell issues have been stud-ied by references 9,10,6,8, and 12 (among others)and we hope to take advantage of this investment.Thirdly, this work investigates a multigrid strategy that isspecialized for adaptively refined Cartesian meshes. In ourapproach, all grids in the multigrid hierarchy cover the entiredomain and include cells at many refinement levels. Thesmoother therefore iterates over the entire domain when it isinvoked on any grid in the hierarchy. In this respect, theapproach shares more with agglomeration or algebraic multi-grid techniques than with many other Cartesian or AMRmethods which iterate over only cells at the same level ofrefinement