Abstract:
An algebraic approach to the design of nonlinear high-resolution finite element schemes is revisited and applied to a variety of multiphase flow problems. In particular, an algebraic flux correction scheme of TVD type is used to simulate the flow of two immiscible incompressible fluids by the level set method. The numerical examples to be presented include a 2D simulation of rising bubbles merging with a free surface as well as drop formation from a liquid stream. A new benchmark problem that involves the rise of a single bubble is described in detail. Reference solutions and numerical results are presented for the circularity, center of mass, and mean rise velocity of the bubble. A macroscopic two-fluid model is presented for turbulent bubbly flows in gas-liquid reactors. The influence of mass transfer and chemical reactions on the velocity field is illustrated by numerical examples. Coalescence and breakup phenomena are taken into account using a detailed population balance model for the bubble size distribution. Last but not least, some promising research directions (multiphase flows in porous media, anisotropic diffusion problems) are discussed.
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