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CAD‐consistent adaptive refinement using a NURBS‐based discontinuous Galerkin method
Author(s) -
Duvigneau Régis.
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4819
Subject(s) - inviscid flow , discontinuous galerkin method , computational fluid dynamics , computation , galerkin method , computer science , adaptive mesh refinement , compressible flow , compressibility , spline (mechanical) , cad , mathematics , supersonic speed , algorithm , mathematical optimization , computational science , finite element method , mechanics , physics , engineering drawing , engineering , thermodynamics , structural engineering
Summary This study concerns the development of a new method combining high‐order computer‐aided design (CAD)‐consistent grids and adaptive refinement/coarsening strategies for efficient analysis of compressible flows. The proposed approach allows to use geometrical data from CAD without any approximation. Thus, the simulations are based on the exact geometry, even for the coarsest discretizations. Combining this property with a local refinement method allows to start computations using very coarse grids and then relies on dynamic adaption to construct suitable computational domains. The resulting approach facilitates interactions between CAD and computational fluid dynamics solvers and focuses the computational effort on the capture of physical phenomena, since geometry is exactly taken into account. The proposed methodology is based on a discontinuous Galerkin method for compressible Navier‐Stokes equations, modified to use nonuniform rational B‐Spline representations. Local refinement and coarsening are introduced using intrinsic properties of nonuniform rational B‐Spline associated with a local error indicator. A verification of the accuracy of the method is achieved and a set of applications are presented, ranging from viscous subsonic to inviscid trans‐ and supersonic flow problems.