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''

On the adjoint solution of the quasi-1D Euler equations: the effect of boundary conditions and the numerical flux function

This work compares a numerical and analytical adjoint equation method with respect to boundary condition treatments applied to the quasi-1D Euler equations. The effect of strong and weak boundary conditions and the effect of flux evaluators on the numerical adjoint solution near the boundaries are discussed

Comparison of two adjoint equation approaches with respect to boundary-condition treatments for the quasi-1D Euler equations

For computation of nonlinear aeroelastic problems, an efficient error estimation and grid adaptation algorithm is highly desirable, but traditional error estimation or grid adaptation do not suffice, since they are insufficiently related to relevant engineering variables and are incapable of significantly reducing the computing time. The dual formulation however, can be used as an a-posteriori error estimation in the quantity of interest. However, derivation of the dual problem, especially the accompanying boundary conditions, is not a trivial task. This document compares a discrete and analytical ad joint equation method with respect to boundary-condition treatments applied on the quasi-1D Euler equations. Flux evaluation of the primal problem is do ne by a Linearised Godunov scheme. For our future goal, solving ftuid-structure problems, the discrete approach seems preferable

On the adjoint solution of the quasi-1D Euler equations: the effect of boundary conditions and the numerical flux function

This work compares a numerical and analytical adjoint equation method with respect to boundary condition treatments applied to the quasi-1D Euler equations. The effect of strong and weak boundary conditions and the effect of flux evaluators on the numerical adjoint solution near the boundaries are discussed

On the adjoint solution of the quasi-1D Euler equations: the effect of boundary conditions and the numerical flux function

This work compares a numerical and analytical adjoint equation method with respect to boundary condition treatments applied to the quasi-1D Euler equations. The effect of strong and weak boundary conditions and the effect of flux evaluators on the numerical adjoint solution near the boundaries are discussed