Seminarreihe "structure preserving numerical methods for hyperbolic equations" im Oberseminar Mathematische Strömungsmechanik: Claus-Dieter Munz

This talk is part of the seminar series "structure preserving numerical methods for hyperbolic equations", click here for more details 

Abstract:

The numerical modelling of evaporation in a two-phase fluid is difficult within a continuum description because the equation of state is non- convex in the spinodal region. Approximating the phase transition as a discontinuity in a macroscopic description allows to introduce an additional wave - an evaporation wave –where appropriate jump conditions hold. The structure of the Riemann problem solution is preserved though we have four waves with three equations. By imposing jump conditions that satisfy a so-called kinetic relation, taking into account local thermodynamics and heat conduction at the interface, the non-physical states in the spinodal region can be avoided and a proper solution can be determined. We apply this two-phase Riemann solution as well as an approximate two- phase Riemann solver within a sharp interface approximation based on a ghost fluid approach. We compare simulations for benchmark Riemann problems with phase change with results from molecular dynamics. A truncated and shifted Lennard-Jones potential in molecular dynamics allows long time and large space scale simulations to approach the macroscopic scales. A highly accurate deduced equation of state for the Euler equations establishes a one-to-one correspondence of the molecular dynamics and the continuum solutions.

via Zoom video conference (request the Zoom link from klingen@mathematik.uni-wuerzburg.de)