FLUX DIFFERENCE SPLITTING FOR THREE-DIMENSIONAL STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN CURVILINEAR CO-ORDINATES

Autor: Cornelis W. Oosterlee, H. Ritzdorf
Rok vydání: 1996
Předmět:
Zdroj: International Journal for Numerical Methods in Fluids. 23:347-366
ISSN: 1097-0363
0271-2091
DOI: 10.1002/(sici)1097-0363(19960830)23:4<347::aid-fld424>3.0.co;2-o
Popis: SUMMARY A collocated discretization of the 3D steady incompressible Navier-Stokes equations based on a flux-difference- splitting formulation is presented. The discretization employs primitive variables of Cartesian velocity components and pressure. The splitting used here is a polynomial splitting introduced by Dick and Linden of Roe type. Second-order accuracy is obtained with the defect correction approach in which the state vector is inter- polated with van Leer's ic-scheme. The underlying solution technique to solve the discretized equations is a parallel multiblock multigrid method. Several 2D and 3D test problems such as driven cavity and channel flows are solved. For the discretization and solution of the steady incompressible Navier-Stokes equations in arbitrarily shaped domains, several methods have been proposed. With the finite element method, very complex geometries can be discretized. However, for solving finite element dicretizations, it is a disadvantage that the sparsity pattern of a discretized operator is not regular. Therefore it can be difficult to find robust solution methods. A compromise between flexibility and robustness is the use of finite volume discretizations on block-structured grids. In a general domain, then, a boundary-fitted curvilinear grid is generated. With multiblock methods the flexibility of these finite volume methods is increased. The regular sparsity pattern in these discretizations can be employed for robustness and efficiency aspects of solution methods. The discretization methods adopting boundary-fitted curvilinear co-ordinate systems differ in grid arrangement (collocated or staggered grids) and in the choice of velocity components (Cartesian or so-called grid-oriented velocity unknowns such as contravariant components). Nowadays, discretization techniques that have proved to be successful and promising for 2D problems are being generalized to three dimensions. An (incomplete) overview of some of these techniques is given now. The first approach where complex flows are solved successfully employs a combination of staggered grids and contravariantflux unknowns and pressure as dependent variables. It is for example used in References 1 and 2, where also 3D problems were tackled. The same combination was used in a different fashion in Reference 3, for which 3D flow was shown in Reference 4. Another recent paper CCC 027 1-209 1 /96/04O347-20
Databáze: OpenAIRE
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