Adaption of a two phase solver for axisymmetric problems

Abstract

This report documents the adaptation of a two dimensional two phaseNavier-Stokes solver to axisymmetric problems. The changes fromCartesian to cylindrical coordinates are thoroughly described with finitedifference methods for the heat equation, Poisson equation, singleand two phase Navier-Stokes equations.The jump conditions at interfacesare modified to accommodate these changes for the two phaseNavier-Stokes equations.The changes to the solver are done step by step, and every changeis verified through intermediate test cases with analytical solutions tolimit the possible sources of errors.Finally all stepwise changes are joined together to form an axisymmetrictwo phase Navier-Stokes solver. Results are presented for aresting bubble, and for both viscous and inviscid oscillating ellipticbubbles.