A Kinetic Scheme for Transient Mixed Flows in Non Uniform Closed Pipes: A Global Manner to Upwind All the Source Terms

We present a numerical kinetic scheme for an unsteady mixed pressurized and free surface model. This model has a source term depending on both the space variable and the unknown U of the system. Using the Finite Volume and Kinetic (FVK) framework, we propose an approximation of the source terms following the principle of interfacial upwind with a kinetic interpretation. Then, several numerical tests are presented.

[1]  A kinetic scheme for pressurized flows in non uniform pipes , 2008, 0812.0105.

[2]  Laurent Gosse,et al.  A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservati , 2001 .

[3]  Christian Bourdarias,et al.  A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes , 2008 .

[4]  A kinetic scheme for pressurised flows in non uniform closed water pipes , 2008 .

[5]  B. Perthame,et al.  A kinetic equation with kinetic entropy functions for scalar conservation laws , 1991 .

[6]  Mehmet Ersoy.  Modélisation, analyse mathématique et numérique de divers écoulements compressibles ou incompressibles en couche mince. , 2010 .

[7]  J. Greenberg,et al.  Analysis and Approximation of Conservation Laws with Source Terms , 1997 .

[8]  Ramaz Botchorishvili,et al.  Equilibrium schemes for scalar conservation laws with stiff sources , 2003, Math. Comput..

[9]  B. Perthame,et al.  A kinetic scheme for the Saint-Venant system¶with a source term , 2001 .

[10]  Philip L. Roe,et al.  Upwind differencing schemes for hyperbolic conservation laws with source terms , 1987 .

[11]  G. D. Maso,et al.  Definition and weak stability of nonconservative products , 1995 .

[13]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[14]  J. Greenberg,et al.  A well-balanced scheme for the numerical processing of source terms in hyperbolic equations , 1996 .

[15]  Kyōto Daigaku. Sūgakuka.  Lectures in mathematics , 1968 .