Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the present authors’ reference: Numerical Heat Transfer —Part B, vol. 40, pp. 83–97. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. Owing to this modified numerical scheme with surface tension effect, the advanced semi-implicit method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity.
