Automatic Near-Body Domain Decomposition Using the Eikonal Equation

The purpose of this research is to generate high-aspect-ratiocellsfor structuredgridsinthevicinity ofboundariesforwalldominatedphenomenasuchasviscouslayersinaerodynamicapplications.Whensuchdomainsarediscretizedforcomplexgeometries,itisimportantthatthegridfitstheboundarieswell,andthisbecomesevenmoredifficulttoachievewithstronglycurvedboundaries.Domaindecompo-sitionsimplifiesthisproblemby subdividingthedomainintomultipleblocksandmakesthetaskofmeshingcomplexgeometriesmoremanageable.Therearemanybenefitstousingamulti-block strategy.Itispossibletocon-trol the orthogonalityand grid quality more preciselywithin smallerblocks, anditallowsdifferentmeshtypesandgenerationtechniquesineachindividualblock.Also,parallelalgorithmscanbeembeddedinthemeshgenerationalgorithm,wheredifferentblockscanbeassignedtodifferentprocessors,thusgreatlyimprovingtheefficiencyoftheprocess.Thepresentpaperintroducesanapproachtoautomaticallydecomposeanarbi-trarycomplexdomainintoface-matchingmulti-blocksemanatingfromthebound-aries.Thesubdivisionprocedureisbasedonthecreationofoffsetsurfaceswhichcloselyfittheir geometries instead of arbitrary planes or surfaces. Thisfitting isachievedthroughaweaksolutionoftheOffsetDistanceFunction,whichisavaria-tionoftheEikonalequation.Computingthenormaldirectionsinthismannerinsuresthattheydonotcross,andtheresultingpropagationavoidsself-intersectionswhicharisefromdirectconstructionmethods.Thusthismethodcanbeappliedonanarbitrarycomplexdomain,i.e.,acon-cave,oraconvexshape, it mayhave sharp corners, or even bemulti-connected.Inaddition,theproposedmethodtransportstheoriginalparameterizationtothepropagated surface whichallows rigorousmatching of block faces. The geometricand topological configurations are thus well defined whichallows to increasetheautomationlevelwithoutuserintervention.

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