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| HAL: hal-00390075, version 1 |
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| Available versions: | v1 (2009-06-01) | v2 (2010-01-28) | v3 (2012-05-09) |
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| The algebraic immersed interface and boundary method for elliptic equations with discontinuous coefficients |
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| Arthur Sarthou 1Stéphane Vincent 1 |
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| (2009-04-15) |
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| A new immersed interface method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface problems. This method allows accurate discontinuous conditions on immersed boundaries and interfaces to be imposed. The main idea is to create auxiliary unknowns at existing grid locations in order to increase the degrees of freedom of the initial problem. These auxiliary nodes allow to impose various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients at a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured or unstructured grid code. Several validation problems are presented to demonstrate the interest and accuracy of the method. |
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| 1: | Transferts, écoulements, fluides, énergétique (TREFLE) |
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CNRS : UMR8508 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB) – Arts et Métiers ParisTech |
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| 2: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Subject | : | Computer Science/Modeling and Simulation Mathematics/Numerical Analysis Physics/Physics/Computational Physics |
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| Fictitious domain – Immersed interface method – Penalty methods – Heat transfert – Finite volumes – Elliptic equations – Immersed boundary method. |
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| Attached file list to this document: | |||||
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| hal-00390075, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00390075 | |
| oai:hal.archives-ouvertes.fr:hal-00390075 | |
| From: Arthur Sarthou | |
| Submitted on: Sunday, 31 May 2009 21:46:32 | |
| Updated on: Monday, 1 June 2009 21:12:58 | |
