##
**Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces.**
*(English)*
Zbl 0994.76050

Summary: We present the stabilized-finite-element/interface-capturing (SFE/IC) method developed for parallel computation of unsteady flow problems with two-fluid interfaces and free surfaces. The SFE/IC method involves stabilized formulations, an interface-sharpening technique, and the enforcement of global mass conservation for each fluid. The SFE/IC method has been efficiently implemented on the CRAY T3E parallel supercomputer. A number of two-dimensional test problems are presented to demonstrate how the SFE/IC method works and the accuracy it attains. We also show how the SFE/IC method can be effectively applied to three-dimensional simulations of challenging flow problems, such as two-fluid interfaces in a centrifuge tube and operational stability of a partially filled tanker truck driving over a bump.

### MSC:

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

76D05 | Navier-Stokes equations for incompressible viscous fluids |

65Y05 | Parallel numerical computation |

### Keywords:

stabilized-finite-element/interface-capturing method; two-fluid interfaces; free surfaces; interface-sharpening technique; global mass conservation; CRAY T3E parallel supercomputer; centrifuge tube; partially filled tanker truck
PDF
BibTeX
XML
Cite

\textit{S. Aliabadi} and \textit{T. E. Tezduyar}, Comput. Methods Appl. Mech. Eng. 190, No. 3--4, 243--261 (2000; Zbl 0994.76050)

Full Text:
DOI

### References:

[1] | Aliabadi, S.K.; Tezduyar, T.E., Space-time finite element computation of compressible flows involving moving boundaries and interfaces, Computer methods in applied mechanics and engineering, 107, 209-223, (1993) · Zbl 0798.76037 |

[2] | Behr, M.; Tezduyar, T.E., Finite element solution strategies for large-scale flow simulations, Computer methods in applied mechanics and engineering, 112, 3-24, (1994) · Zbl 0846.76041 |

[3] | Johnson, A.A.; Tezduyar, T.E., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Computer methods in applied mechanics and engineering, 119, 73-94, (1994) · Zbl 0848.76036 |

[4] | 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 tests, Computer methods in applied mechanics and engineering, 94, 339-351, (1992) · Zbl 0745.76044 |

[5] | Tezduyar, T.E.; Behr, M.; Mittal, S.; Liou, J., 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, Computer methods in applied mechanics and engineering, 94, 353-371, (1992) · Zbl 0745.76045 |

[6] | G. Wren, S. Ray, S. Aliabadi, T. Tezduyar, Simulation of flow problems with moving mechanical components, fluid – structure interactions and two-fluid interfaces, International Journal for Numerical Methods in Fluids (1997), to appear · Zbl 0881.76054 |

[7] | Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Kalro, V.; Litke, M., Flow simulation and high performance computing, Computational mechanics, 18, 397-412, (1996) · Zbl 0893.76046 |

[8] | Aliabadi, S.K.; Tezduyar, T.E., Parallel fluid dynamics computations in aerospace applications, International journal for numerical methods in fluids, 21, 783-805, (1995) · Zbl 0862.76033 |

[9] | Hirt, C.W.; Nichols, B.D., Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of computational physics, 39, 201-225, (1981) · Zbl 0462.76020 |

[10] | D.L. Youngs, Time-dependent multimaterial flow with large fluid distortion, in: K.W. Morton, M.J. Baines (Eds.), Numerical Methods in Fluid Dynamics, Notes on Numerical Fluid Mechanics, Academic Press, New York, 1984, pp. 273-285 |

[11] | Lemos, C.M., Higher-order schemes for free-surface flows with arbitrary configurations, International journal for numerical methods in fluids, 23, 545-566, (1996) · Zbl 0897.76063 |

[12] | S. Aliabadi, T. Tezduyar, 3D simulation of free-surface flows with parallel finite element method, in: Computational Mechanics ’97, Proceedings of International Conference on Computational Engineering Science, San Jose, Costa Rica, 1997, to appear |

[13] | T.E. Tezduyar, S. Aliabadi, M. Behr, Enhanced-discretization interface-capturing technique, in: Y. Matsumoto, A. Prosperetti (Eds.), Proceedings of the ISAC ’97 High Performance Computing on Multiphase Flows, Japan Society of Mechanical Engineers, 1997, pp. 1-6 · Zbl 0961.76046 |

[14] | T.E. Tezduyar, S. Aliabadi, M. Behr, Parallel finite element computing methods for unsteady flows with interfaces, Computational Fluid Dynamics Review 1997, to appear |

[15] | T.E. Tezduyar, S. Aliabadi, M. Behr, Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces, Computer Methods in Applied Mechanics and Engineering (1997), to appear · Zbl 0961.76046 |

[16] | Brooks, A.N.; Hughes, T.J.R., Streamline upwind/petrov – galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier – stokes equations, Computer methods in applied mechanics and engineering, 32, 199-259, (1982) · Zbl 0497.76041 |

[17] | Tezduyar, T.E., Stabilized finite element formulations for incompressible flow computations, Advances in applied mechanics, 28, 1-44, (1991) · Zbl 0747.76069 |

[18] | Johan, Z.; Hughes, T.J.R.; Shakib, F., A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids, Computer methods in applied mechanics and engineering, 87, 281-304, (1991) · Zbl 0760.76070 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.