A monolithic mass tracking formulation for bubbles in incompressible flow

摘要: Abstract We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation state order to determine pressure boundary conditions inside each bubble. show executing this algorithm traditional manner leads stability issues similar those seen partitioned methods solid–fluid coupling. Therefore, we reformulate problem monolithically. This is accomplished by first proposing new fully monolithic approach coupling nonlinear compressible including effects shocks rarefactions, then subsequently making number simplifying assumptions air removing not only nonlinearities but also spatial variations both density pressure. The resulting quite robust, has been shown converge known solutions test problems, be effective more realistic problems with multiple bubbles, merging pinching, etc. Notably, departs from standard two-phase model where preserves its volume despite potentially large forces differentials surrounding fluid should change volume. Our readily according isothermal state.