Volume 13, Issue 1
The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions

Mohamed Kara, Salim Mesbahi & Philippe Angot

Adv. Appl. Math. Mech., 13 (2021), pp. 119-139.

Published online: 2020-10

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  • Abstract

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem, the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method. The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain. Here, we present a cell-centered finite volume method to discretize the fictitious domain problem. The proposed method is numerically validated for different test cases. This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

  • Keywords

Fictitious domain method, sharp interface, elasticity system, jump embedded boundary conditions, finite volume method.

  • AMS Subject Headings

65M55, 65N08, 65N85

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-119, author = {Mohamed Kara , and Salim Mesbahi , and Philippe Angot , }, title = {The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {1}, pages = {119--139}, abstract = {

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem, the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method. The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain. Here, we present a cell-centered finite volume method to discretize the fictitious domain problem. The proposed method is numerically validated for different test cases. This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0119}, url = {http://global-sci.org/intro/article_detail/aamm/18343.html} }
TY - JOUR T1 - The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions AU - Mohamed Kara , AU - Salim Mesbahi , AU - Philippe Angot , JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 119 EP - 139 PY - 2020 DA - 2020/10 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0119 UR - https://global-sci.org/intro/article_detail/aamm/18343.html KW - Fictitious domain method, sharp interface, elasticity system, jump embedded boundary conditions, finite volume method. AB -

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem, the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method. The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain. Here, we present a cell-centered finite volume method to discretize the fictitious domain problem. The proposed method is numerically validated for different test cases. This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

Mohamed Kara, Salim Mesbahi & Philippe Angot. (2020). The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions. Advances in Applied Mathematics and Mechanics. 13 (1). 119-139. doi:10.4208/aamm.OA-2019-0119
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