Study of Conservation on Implicit Techniques for Unstructured Finite Volume Navier-Stokes Solvers


  • Carlos Junqueira-Junior Instituto Tecnológico de Aeronáutica
  • Leonardo Costa Scalabrin EMBRAER SA.
  • Edson Basso Instituto de Aeronáutica e Espaço
  • João Luiz F. Azevedo Instituto de Aeronáutica e Espaço


Computational fluid dynamics, Time marching methods, Flux vector splitting scheme, Conservative discretization.


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  non-conservative 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 to evaluate the conservation of implicit and explicit time-marching methods and discusses numerical requirements that can help avoiding such  non-conservation issues.

Author Biographies

Carlos Junqueira-Junior, Instituto Tecnológico de Aeronáutica

São Paulo

Leonardo Costa Scalabrin, EMBRAER SA.

São José dos Campos - São Paulo

Edson Basso, Instituto de Aeronáutica e Espaço

São José dos Campos - São Paulo

João Luiz F. Azevedo, Instituto de Aeronáutica e Espaço

São José dos Campos - São Paulo






Original Papers