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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2015010454
pages 65-79

STUDY OF CONSERVATION APPLIED TO POINT-IMPLICIT INTEGRATION TECHNIQUES FOR UNSTRUCTURED FINITE VOLUME NAVIER−STOKES SOLVERS

Carlos Junqueira-Junior
Instituto Tecnologico de Aeronautica − ITA, Sao Jose dos Campos, SP, Brazil
Leonardo Costa Scalabrin
EMBRAER S.A., Sao Jose dos Campos, SP, Brazil
Edson Basso
Instituto de Aeronautica e Espaco − IAE, Sao Jose dos Campos, SP, Brazil
Joao Luiz F. Azevedo
Instituto de Aeronautica e Espaco − IAE, Sao Jose dos Campos, SP, Brazil

ABSTRAKT

The work is a study of conservation on linearization techniques of time-marching schemes for the unstructured finite volume Reynolds-averaged Navier−Stokes formulation. The solver used in this work calculates the numerical flux applying an upwind discretization based on the flux vector splitting scheme. This numerical treatment results in a very large sparse linear system. The direct solution of this full implicit linear system is very expensive and, in most cases, impractical. There are several numerical approaches which are commonly used by the scientific community to treat sparse linear systems, and the point-implicit integration was selected in the present case. However, numerical approaches to solve implicit linear systems can be nonconservative in time, even for formulations which are conservative by construction, as the finite volume techniques. Moreover, there are physical problems which strongly demand conservative schemes in order to achieve the correct numerical solution. The work presents results of numerical simulations of closed domain concerning the evaluation of the mass conservation on implicit and explicit time-marching methods using constant and variable time steps. The explicit integration, with the use of a constant time step all over the domain, has preserved the conservative characterist of the finite volume formulation whereas the point-implicit integration requires numerical treatement in order to avoid such nonconservation issues.


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