### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 44 |

Publication status | Published - Aug 2007 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | LNCS4549/1849 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-64317
- METIS-241868
- EWI-10964
- space-time
- interface tracking
- level set method
- two fluid flows
- Discontinuous Galerkin finite element method
- Cut-cell method

### Cite this

*A space-time discontinuous Galerkin finite element method for two-fluid problems*. (Memorandum / Department of Applied Mathematics; No. LNCS4549/1849). Enschede: University of Twente, Department of Applied Mathematics.

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*A space-time discontinuous Galerkin finite element method for two-fluid problems*. Memorandum / Department of Applied Mathematics, no. LNCS4549/1849, University of Twente, Department of Applied Mathematics, Enschede.

**A space-time discontinuous Galerkin finite element method for two-fluid problems.** / Sollie, W.E.H.; van der Vegt, Jacobus J.W.; Bokhove, Onno.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - A space-time discontinuous Galerkin finite element method for two-fluid problems

AU - Sollie, W.E.H.

AU - van der Vegt, Jacobus J.W.

AU - Bokhove, Onno

PY - 2007/8

Y1 - 2007/8

N2 - A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy. The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux.

AB - A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy. The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux.

KW - IR-64317

KW - METIS-241868

KW - EWI-10964

KW - space-time

KW - interface tracking

KW - level set method

KW - two fluid flows

KW - Discontinuous Galerkin finite element method

KW - Cut-cell method

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - A space-time discontinuous Galerkin finite element method for two-fluid problems

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -