A continuously differentiable upwinding scheme for the simulation of fluid flow problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Processo FAPESP: 04/16064-9

Processo FAPESP: 06/00480-9

Processo FAPESP: 09/16954-8

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier B.V. All rights reserved.