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Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes

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Communications in Computational Physics 2022年第6期32卷 259-298页

作者： Walter Boscheri Michael Dumbser Elena Gaburro Department of Mathematics and Computer Science University of FerraraVia Machiavelli 3044121 FerraraItaly Department of Civil Environmental and Mechanical EngineeringUniversity of TrentoVia Mesiano 7738123 TrentoItaly Inria Univ.BordeauxCNRSBordeaux INPIMBUMR 5251200 Avenue de la Vieille Tour33405 Talence cedexFrance

We propose a new high order accurate nodal discontinuous Galerkin(DG)method for the solution of nonlinear hyperbolic systems of partial differential equations(PDE)on unstructured polygonal Voronoi *** than using classical polynomials of degree N inside each element,in our new approach the discrete solution is represented by piecewise continuous polynomials of degree N within each Voronoi element,using a continuous finite element basis defined on a subgrid inside each *** call the resulting subgrid basis an agglomerated finite element(AFE)basis for the DG method on general polygons,since it is obtained by the agglomeration of the finite element basis functions associated with the subgrid *** basis functions on each sub-triangle are defined,as usual,on a universal reference element,hence allowing to compute universal mass,flux and stiffness matrices for the subgrid triangles once and for all in a pre-processing stage for the reference element ***,the construction of an efficient quadrature-free algorithm is possible,despite the unstructured nature of the computational *** order of accuracy in time is achieved thanks to the ADER approach,making use of an element-local space-time Galerkin finite element *** novel schemes are carefully validated against a set of typical benchmark problems for the compressible euler and navier-stokes *** numerical results have been checked with reference solutions available in literature and also systematically compared,in terms of computational efficiency and accuracy,with those obtained by the corresponding modal DG version of the scheme.

关键词： Continuous finite element subgrid basis for DG schemes high order quadraturefree ADER-DG schemes unstructured Voronoi meshes comparison of nodal and modal basis compressible euler and navier-stokes equations

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