Implicit Boundary Treatment for Joined and Disjoint Patched Mesh Systems
The CSCM flux difference eigenvector split upwind scheme for the compressible Euler or Navier-Stokes equation is adapted to solve the problem of capturing embedded flow structures with high resolution on systems of aligned overset meshes.
Characteristics based upwind operationally explicit implicit difference relations with diagonally dominant approximate factorization are argued to be appropriate for compatibly and stably exchanging data in the vicinity of interior patch boundaries through simple interpolation of conservative variable data. Particular interpolation procedures are advocated that involve only positive weights and interpolant data with consistent upwind domain of dependence with respect to the receiving grid. A linearly equilvalent procedure involving interpolation of needed flux components is given and argued to be somewhat more accurate in the vicinity of discontinuities. With minimal overlap, sections on the coarse mesh that underly overset refinements are removed from the computation. The resulting segmented mesh data structure leads to interesting opportunities including nonaligned mesh-boundary intersections which we exploit for high resolution capture of shock reflections.
Factors in accuracy of the flow structure adaptive patching technique are demonstrated in an inviscid supersonic inlet problem involving weak shocks and an expansion fan. In the context of that two dimensional problem with shock aligned patched meshing, it is found that similar accuracy can be achieved with a savings of an order of magnitude in computed points relative to uniformly refined mesh.
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