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Three-dimensional adaptive Cartesian grid method with conservative interface restructuring and reconstruction. (English) Zbl 1248.76111
Summary: Multiphase flows associated with interfacial dynamics, steep jumps in fluid properties and moving boundaries between different phases pose substantial computational challenges in terms of both modeling as well as computational efficiency. The present work extends a marker-based immersed boundary, or front tracking, technique to model the three-dimensional interfacial dynamics. It tracks the moving boundary using triangulated surface grids and solves the flow equations on a stationary Cartesian grid. A locally adaptive grid is employed to help meet the resolution requirements based on the interface location and solution features. The interface resolution is controlled via a conservative restructuring technique satisfying mass continuity. An improved level contour reconstruction algorithm for topology change, preserving the interface connectivity information, is presented highlighting various algorithmic difficulties and implemented remedies. The outlines of a finite volume staggered grid Navier-Stokes solution using the projection method are discussed. The impact of conservative interface restructuring and reconstruction has been assessed against mass conservation and spurious velocity errors. The overall capabilities of the developed algorithms have been demonstrated for large density ratios, $$O(1000)$$, interfacial flows using various rising bubbles and drop collision/coalescence computations involving coalescence and break-up dynamics.

##### MSC:
 76M12 Finite volume methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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