Improved capturing of contact discontinuities for two-fluid flows

Past years, there has been much research in extending and applying approximate Riemann solvers to immiscible two-fluid flows, more and more often in combination with a level-set technique to improve the resolution of the interface(s) between the two fluids. The interfaces are contact discontinuities. Accurately capturing contact discontinuities is harder than capturing shock waves, because of the lack of a steepening mechanism. Moreover, a known difficulty in computing flows with contact discontinuities in the usual conservative formulation is that zeroth-order pressure errors may arise. (This interesting numerical feature is fully understood; it appears to be independent of the monotonicity and accuracy properties of the time and space discretization.) Several remedies against the pressure errors have been proposed already. This MSc work consists of computations of a two-fluid interface moving in a tube: first without pressure-oscillation fix (to see how serious the pressure oscillations really are) and next, with fixes. The used approximate methods are the ghost-fluid method and a new method, called the mass-fraction method. Also, an exact two-fluid Riemann solver has been derived and implemented in a software program, called ``Visual Shock Tube Solver''.