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An Implicit Finite Volume Approach of the k ‐ ε Turbulence Model on Unstructured Grids
Author(s) -
Meister Andreas,
Obermann Micheal
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199811)78:11<743::aid-zamm743>3.0.co;2-i
Subject(s) - finite volume method , discretization , mathematics , linearization , linear system , context (archaeology) , turbulence , krylov subspace , upwind scheme , computation , mathematical analysis , algorithm , physics , nonlinear system , mechanics , paleontology , quantum mechanics , biology
This paper is devoted to the development of a finite volume method for the computation of turbulent flow fields on unstructured grids. The discretization of the inviscid fluxes is accomplished by means of the modern upwind scheme AUSMDV [35], whereby linear ansatz functions are considered on each control volume to achieve high resolution properties. Furthermore, a central scheme is used for the approximation of the viscous fluxes. The involved operator splitting technique leads to low memory requirement, yields high flexibility concerning the use of particular turbulence models, and preserves a possibly included second order time discretization. The time discretization is performed is an implicit manner, which enables large time steps in comparison with an explicit formulation. The linearization of the numerical flux functions as well as the turbulent and axisymmetric source terms leads to a linear system of equations including a large, sparse, and nonsymmetric matrix. Recently, a systematic investigation and comparison of different preconditioned Krylov subspace methods in the context of real engineering applications was presented [18]. Based on these results, the BiCGSTAB algorithm [31] preconditioned by an incomplete LU factorization is used to solve the linear system of equations. The scheme is finally validated on specific test cases, whereby the results are compared with experimental data, analytical solutions, and numerical simulations of other authors.