A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes. (English) Zbl 1152.76020
Summary: The aim is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) the energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case the energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.
MSC:
| 76B99 | Incompressible inviscid fluids |
| 76M30 | Variational methods applied to problems in fluid mechanics |
References:
| [1] | Botchorishvili, R.; Perthame, B.; Vasseur, A., Equilibrium schemes for scalar conservation laws with stiff sources, Math. Comp., 72, 241, 131-157 (2003) · Zbl 1017.65070 |
| [2] | Bourdarias, C.; Gerbi, S., An implicit finite volumes scheme for unsteady flows in deformable pipe-lines, (Herbin, R.; Kröner, D., Finite Volumes for Complex Applications. III: Problems and Perspectives (2002), Hermes Science Publications), 463-470 · Zbl 1177.76212 |
| [3] | C. Bourdarias, S. Gerbi, A conservative model for unsteady flows in deformable pipe-lines and its implicit second order finite volume discretisation. Comput. Fluids, to appear.; C. Bourdarias, S. Gerbi, A conservative model for unsteady flows in deformable pipe-lines and its implicit second order finite volume discretisation. Comput. Fluids, to appear. · Zbl 1237.76081 |
| [4] | Bourdarias, C.; Gerbi, S., A finite volume scheme for a model coupling free surface and pressurised flows in pipes, J. Comput. Appl. Math., 209, 1, 109-131 (2007) · Zbl 1135.76036 |
| [5] | H. Capart, X. Sillen, Y. Zech, Numerical and experimental water transients in sewer pipes, J. Hydraulic Res. (1997) 659-672.; H. Capart, X. Sillen, Y. Zech, Numerical and experimental water transients in sewer pipes, J. Hydraulic Res. (1997) 659-672. |
| [6] | N.T. Dong, Sur une méthode numérique de calcul des écoulements non permanents soit à surface libre, soit en charge, soit partiellement à surface libre et partiellement en charge, La Houille Blanche (1990) 149-158.; N.T. Dong, Sur une méthode numérique de calcul des écoulements non permanents soit à surface libre, soit en charge, soit partiellement à surface libre et partiellement en charge, La Houille Blanche (1990) 149-158. |
| [7] | Perthame, B.; Simeoni, C., A kinetic scheme for the Saint-Venant system with a source term, Calcolo, 38, 4, 201-231 (2001) · Zbl 1008.65066 |
| [8] | Streeter, V. L.; Wylie, E. B.; Bedford, K. W., Fluid Mechanics (1998), McGraw-Hill: McGraw-Hill New York |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
