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  4. The "dam-break" problem for a two-layer (a...

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Partial differential Equations, Numerics and Control

The "dam-break" problem for a two-layer (air and water) model conditionally hyperbolic.

Mehmet Ersoy

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We simulate an air entrainment by a system of four partial differential equations which is conditionnaly hyperbolic. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas).

Several finite volume method fails to compute the solution accurately when the system loss its hyperbolicity. The main raison is that when the system is hyperbolic, the eigenvalues are first obtained as an approximation (with respect to the relative layer speed) and secondly the accuracy when the system loss its hyperbolic leads to unstable numerical scheme even if the mesh is small.

We propose a new approach based on the kinetic scheme, that we call "the two-layer kinetic scheme" which first does not requires the computation of the eigenvalues and it is stable with respect to the meshsize even if the system is almost everywhere hyperbolic in space and in time.

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Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)