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Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monte-Ampère equation. (English) Zbl 1141.76043
Summary: We review some recent applications of operator-splitting methods. We show that these methods are well-suited to the numerical solution of outstanding problems from various areas in mechanics, physics and differential geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and elliptic real Monge-Ampère equation. The results of numerical experiments illustrate the capabilities of these methods.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
76D45 Capillarity (surface tension) for incompressible viscous fluids
65N99 Numerical methods for partial differential equations, boundary value problems
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