In this study, we have implemented the sharp interface algorithm with the existing schemes, i.e. A robust MUSCL type AUSMD and THINC schemes which employs a approximated Riemann solver along with the Tangent of Hyperbola for Interface Capturing (THINC) technique to reconstruct the solution function for both smooth profile and discontinuity. The basic idea is to reconstruct the solution functions so that the jumps at cell boundaries are minimized, which effectively reduces the numerical dissipation in the resulting schemes. The THINC reconstruction automatically realizes the highest possible polynomial interpolation for smooth profile, whilst prefers other forms of reconstructions in the presence of discontinuities. The concept is a general platform of more profound impact can be used with other candidate reconstructions to further explore high-fidelity schemes for capturing both smooth and discontinuous solutions. Here, to consider the multi-component flow equations, the mixture model is regarded as a model equation. The transport equation for each volume fraction is expressed in quasi-conservative form. Numerical model is not only demonstrated to maintain pressure equilibrium over contact discontinuities using conservative pressure update, but also AUSMD are shown to enhance pressure being continuous across the contact discontinuity by means of a blend function of the ratio of pressure to density As shown in Excellent preliminary numerical results have been obtained for the Euler conservation laws, which the 2-D shock-cylinder interaction problem involves shock waves, material interfaces and their interaction.
Third Computational Mechanics Conference in Taiwan