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Computation of unsteady flows with mixed finite volume/finite element upwind methods
Author(s) -
Debiez Christophe,
Dervieux Alain,
Mer Katherine,
Nkonga Boniface
Publication year - 1998
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/(sici)1097-0363(199801)27:1/4<193::aid-fld659>3.0.co;2-d
Subject(s) - finite volume method , computation , finite element method , polygon mesh , upwind scheme , mathematics , advection , computational fluid dynamics , vortex , numerical diffusion , mechanics , geometry , mathematical analysis , physics , algorithm , discretization , thermodynamics
We refer to as mixed element/volume (MEV) methods the application of finite element for diffusion terms and finite volume for advection terms in a flow model. The compatibility of these methods can be checked for some low‒order approximations; the resulting schemes may enjoy the relative mesh‒regularity‒independent accuracy of finite element methods as discussed in a first section. In recent years a number of developments (by INRIA Dassault and T. Barth, among others) have produced P1‒continuous schemes that involve some MUSCL/TVD unidirectional limitation; the resulting schemes are very useful but sometimes may involve much more numerical viscosity than necessary, especially for unsteady computations. In the present study, a new version is built by using a larger molecule for the intercell flux evaluation. The 1D version can be promoted to fourth‒ or even fifth‒order spatial accuracy. The 2D version is no better than second‒order‒accurate; however, it involves only a sixth‒order dissipation and the global accuracy is markedly improved even on irregular meshes. The above development extends the ability of the MUSCL/MEV scheme towards the accurate calculation of unsteady flows involving vortex shedding. © 1998 John Wiley & Sons, Ltd.