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**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 0745.76045

Summary: [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### Citations:

Zbl 0745.76044
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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:

[1] | Tezduyar, T. E.; Behr, M.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces—The deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests, Comput. Methods Appl. Mech. Engrg., 94, 339-351 (1992) · Zbl 0745.76044 |

[2] | Hughes, T. J.R.; Franca, L. P.; Mallet, M., A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multidimensional advective-diffusive systems, Comput. Methods Appl. Mech. Engrg., 63, 97-112 (1987) · Zbl 0635.76066 |

[3] | Hughes, T. J.R.; Hulbert, G. M., Space-time finite element methods for elastodynamics: Formulations and error estimates, Comput. Methods Appl. Mech. Engrg., 66, 339-363 (1988) · Zbl 0616.73063 |

[4] | Hughes, T. J.R.; Franca, L. P.; Hulbert, G. M., A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg., 73, 173-189 (1989) · Zbl 0697.76100 |

[5] | Shakib, F., Finite element analysis of the compressible Euler and Navier-Stokes equations, (Ph.D. Thesis (1988), Stanford University) |

[6] | Hansbo, P.; Szepessy, A., A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 84, 175-192 (1990) · Zbl 0716.76048 |

[7] | Hughes, T. J.R.; Liu, W. K.; Zimmermann, T. K., Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Engrg., 29, 329-349 (1981) · Zbl 0482.76039 |

[8] | Liu, W. K.; Chang, H.; Chen, J.-S.; Belytschko, T., Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua, Comput. Methods Appl. Mech. Engrg., 68, 259-310 (1988) · Zbl 0626.73076 |

[9] | Huerta, A.; Liu, W. K., Viscous flow with large free surface motion, Comput. Methods Appl. Mech. Engrg., 69, 277-324 (1988) · Zbl 0655.76032 |

[10] | Liou, J.; Tezduyar, T. E., Computation of compressible and compressible and incompressible flows with the clustered element-by-element method, University of Minnesota Supercomputer Institute Research Report, UMSI 90/215 (October 1990) |

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