A Class Of Upwinding High Resolution Schemes Applied To Two-phase Problems
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In this work, the application of residual distribution schemes (RDS) to two-phase flow problems is described. These schemes have previously given second order precision solutions in steady aeronautical problems. Its implementation in two-phase problems is not straightforward. The analytical models must be hyperbolic, which is not the case, and closed mathematical expressions of the eigenvalues and eigenvectors must be known. Within this context, two different models have been studied. Firstly, we present a well-posed homogeneous model in any configuration of void fractions but with mechanical equilibrium between phases. This model is hyperbolic and the mathematical expressions of the eigenvectors are easily computed. Secondly, we present a two-fluid one pressure model applied to a two-phase flow configuration, without mechanical equilibrium and phase disappearance. The model is not hyperbolic and the analytical expression of the eigenvalues is unknown.