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Finite-volume solvers for a multilayer Saint-Venant system

Audusse E., Bristeau M. O.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 3

311-320

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

Modern finite volume methods solving internal flow problems

Kozel K., Fořt J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2002

Vol. 6, No 1

127-142

The lecture deals with explicit and implicit finite difference and mainly finite volume schemes that have been commonly used in last years for compressible and incompressible fluid flow problems. Mainly we mention schemes used for transonic flow computation (inviscid as well as viscous models) in internal and also external aerodynamics. We prefer modern schemes like RK multistage schemes, TVD and ENO schemes, implicit schemes or higher order schemes. Some results of numerical computation or numerical simulation are presented in the second part of the paper, including 2D and 3D transonic flow through a channel and a cascade (mainly of turbine type), 2D and 3D backward facing step flow (laminar and turbulent), 2D and 3D impinging jet flow (comparisons of some turbulent models). The last two cases have been computed only for incompressible viscous flows. Some tests for the efficiency of higher order scheme (4th-6th order) are presented for the backward facing step problem. In many examples we also present a comparison of numerical and experimental results.