The application of compact residual distribution schemes to two-phase flow problems. (English) Zbl 1242.76335
Summary: The application of residual distribution schemes to two-phase flow problems is described. These schemes have been previously applied to system of conservation laws. However, its implementation in two-phase problems is not straightforward. Different numerical difficulties have been encountered: model hyperbolicity, non-conservative form of the equations, presence of source terms and degenerate cases have been analyzed. Within this context, two different models have been studied. Firstly, we present the Cortes model, where the inclusion of the interface pressure term makes the original system of equations hyperbolic, but there is no analytical expression of the eigenvalues, so linear perturbation methods are applied to obtain the approximate eigenstructure of the system. Secondly, we present the Staedtke model. This model has been designed to be hyperbolic, and analytical expressions of the eigenvectors can be computed. Different one and two dimensional tests have been computed to check the validity of the approach.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
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