On the use of symmetrizing variables for vacuums

Thierry Gallouët (1) , Jean-Marc Hérard (2, 1) , Nicolas Seguin

1 I2M - Institut de Mathématiques de Marseille
2 EDF - EDF

The paper is devoted to the computation of shallow-water equations (or Euler equations) in using an approximate Godunov scheme called VFRoe, when the flow may include dry areas (or very low density regions). This is achieved with the help of symmetrizing variables. Overall we are able to insure the discrete preservation of positive variables on interfaces, and at the same time to compute vacuum occurence or propagation of shock waves over a near-vacuum. A short section is also dedicated to the non-conservative hyperbolic equations arising within the setting of one-equation or two-equation turbulent compressible models. Many numerical tests confirm the capabilities of the scheme, and measuring the L 1 error norm in particular cases enables us to specify the actual rate of convergence.

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]

Thierry Gallouët, Jean-Marc Hérard, Nicolas Seguin. On the use of symmetrizing variables for vacuums. Calcolo, 2003, 40, pp.163-194. ⟨10.1007/s10092-003-0075-0⟩. ⟨hal-04489595⟩