Numerical solver for compressible two-fluid flow

This report treats the development of a numerical solver for the simulation of flows of two non-mixing fluids described by the two-dimensional Euler equations. A level-set equation in conservative form describes the interface. After each time step the deformed level-set function is transformed back to a real signed distance function using a PDE-based redistancing procedure. Interface smoothing is applied to prevent staircasing and possible unphysical oscillations. A finite-volume approximation is used for the numerical solver. The flow model is discretized using a three-stage time marching scheme together with the approximate Riemann solver of Roe. Quadratic sub-cell interpolation is obtained using the limiter by Koren. The combination of time and space discretization makes the method effectively second-order accurate although third-order accuracy can theoretically be reached. The redistancing equation is discretized using a two-stage time-marching scheme and a second-order accurate spatial interpolation. The spurious pressure oscillations due to the numerical inconsistency of conservative level-set methods are removed using a simple 'ghost-fluid like' fix. Several numerical tests are performed to test the solver for its performance. Standard one-dimensional shock tube problems prove the existence of the pressure oscillations and verify the simple fix. A convergence test verifies the numerical order of the scheme. Two-dimensional tests are performed using the shock-bubble interaction problem, the Kelvin-Helmholtz instability and the supersonic free jet