A new strategy for finite element computations involving moving boundaries and interfaces — The deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders.

*(English)*Zbl 0745.76045Summary: [For part I, see the foregoing entry ( Zbl 0745.76044).]

New finite element computational strategies for free-surface flows, two- liquid flows, and flows with drifting cylinders are presented. These strategies are based on the deforming spatial-domain/space-time (DSD/ST) procedure. In the DSD/ST approach, the stabilized variational formulations for these types of flow roblem are written over their space- time domains. One of the important features of the approach is that it enables one to circumvent the difficulty involved in remeshing every time step and thus reduces the projection errors introduced by such frequent remeshings. Computations are performed for various test problems mainly for the purpose of demonstrating the computational capability developed for this class of problems. In some of the test cases, such as the liquid drop problem, surface tension is taken into account. For flows involving drifting cylinders, the mesh moving and remeshing schemes proposed are convenient and reduce the frequency of remeshing.

New finite element computational strategies for free-surface flows, two- liquid flows, and flows with drifting cylinders are presented. These strategies are based on the deforming spatial-domain/space-time (DSD/ST) procedure. In the DSD/ST approach, the stabilized variational formulations for these types of flow roblem are written over their space- time domains. One of the important features of the approach is that it enables one to circumvent the difficulty involved in remeshing every time step and thus reduces the projection errors introduced by such frequent remeshings. Computations are performed for various test problems mainly for the purpose of demonstrating the computational capability developed for this class of problems. In some of the test cases, such as the liquid drop problem, surface tension is taken into account. For flows involving drifting cylinders, the mesh moving and remeshing schemes proposed are convenient and reduce the frequency of remeshing.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76D45 | Capillarity (surface tension) for incompressible viscous fluids |

76V05 | Reaction effects in flows |

##### Keywords:

stabilized variational formulations; liquid drop problem; surface tension; remeshing schemes
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\textit{T. E. Tezduyar} et al., Comput. Methods Appl. Mech. Eng. 94, No. 3, 353--371 (1992; Zbl 0745.76045)

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##### References:

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