A modified semi-implicit method for a hyperbolic two-fluid model

By introducing the interfacial pressure jump terms based on a surface tension into the momentum equations of a two-phase two-fluid model, the mathematical property of the governing equations is changed to a hyperbolic type. Then the eigenvalues of the equation system always become always real values representing the void wave and the pressure wave propagation speeds as shown in the present author's former article: Numerical Heat Transfer – Part B (40) (2001) 83–97. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified by inserting an intermediate calculation process for a void fraction at a fractional time step. This modified semi-implicit method then becomes stable without conventional additive terms. Consequently, by including the interfacial pressure jump terms with the modified semi-implicit method, the numerical calculations of the void discontinuity propagation and water faucet problems can become more stable and sound than those calculated by using virtual mass terms.