数值稳定的可展网格仿真方法(英文)-豆柴文库

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数值稳定的可展网格仿真方法(英文)
Title:NumericallyStableMeshGenerationMethodsforSimulation
Abstract:
Inrecentyears,simulationshavebecomeanindispensabletoolinvariousscientificandengineeringfields.Onefundamentalaspectofsimulatingcomplexsystemsisthegenerationofsuitablecomputationalmeshes.Acomputationallyefficientandaccuratemeshgenerationmethodisessentialforrobustandreliablesimulations.Thispaperexploresthetopicofnumericallystablemeshgenerationmethodsandtheirsignificanceinsimulatingcomplexsystems.
1.Introduction:
Meshgenerationplaysacrucialroleinnumericalsimulationsasitdiscretizesthecomputationaldomainintoacollectionofgeometricalelements,suchastrianglesorquadrilateralsintwodimensions,ortetrahedraorhexahedrainthreedimensions.Theseelementsareusedtosolvethegoverningequationsofthesystemunderinvestigation.However,theprocessofmeshgenerationcanintroducevariousissues,includingnumericalinstability,whichcanleadtoinaccurateandunreliablesimulationresults.
2.ChallengesinMeshGeneration:
Numericalinstabilityinmeshgenerationcanmanifestindifferentforms,suchasmeshtangling,elementdistortion,andill-conditionedJacobianmatrices.Theseissuescanariseduetosingularitiesorgeometriccomplexitiesinthecomputationaldomain.Traditionalmeshgenerationmethods,suchasDelaunaytriangulationoradvancingfrontmethods,maystrugglewiththesechallenges.Therefore,developingnumericallystablemeshgenerationalgorithmsisofutmostimportance.
3.NumericallyStableMeshGenerationMethods:
3.1.AdvancingFrontwithJacobianSmoothing:
Inthismethod,themeshisprogressivelygrownbyextendingthefrontalongtheboundarywhileensuringmeshqualitybasedontheJacobiandeterminant.Regularizationtechniques,suchasJacobiansmoothing,areemployedtostabilizethemeshgenerationprocess.Thismethodisparticularlyeffectiveforhandlingcomplexdomainswithvaryingscales.
3.2.DelaunayRefinementwithMeshOptimization:
Delaunayrefinementalgorithmsstartwithaninitialmeshanditerativelyaddnewelementsbyrefiningtheexistingones.Toensurenumericalstability,additionalgeometricconstraintsandconstraintsonelement