Volume 52, Issue 4
Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid

Cornel Marius Murea

J. Math. Study, 52 (2019), pp. 448-469.

Published online: 2019-12

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  • Abstract

We present a monolithic algorithm for solving fluid-structure interaction. The Updated Lagrangian framework is used for the incompressible neo-hookean structure and Arbitrary Lagrangian Eulerian coordinate is employed for the Navier-Stokes equations. The algorithm uses a global mesh for the fluid-structure domain which is compatible with the fluid-structure interface. At each time step, a non-linear system is solved in a domain corresponding to the precedent time step. It is a semi-implicit algorithm in the sense that the velocity, the pressure are computed implicitly, but the domain is updated explicitly. Using one velocity field defined over the fluid-structure mesh, and globally continuous finite elements, the continuity of the velocity at the interface is automatically verified. The equation of the continuity of the stress at the interface does not appear in this formulation due to action and reaction principle. The stability in time is proved. A second algorithm is introduced where at each time step, only a linear system is solved in order to find the velocity and the pressure. Numerical experiments are presented.

  • Keywords

Fluid-structure interaction, monolithic algorithm, stability.

  • AMS Subject Headings

74F10, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cornel.murea@uha.fr (Cornel Marius Murea)

  • BibTex
  • RIS
  • TXT
@Article{JMS-52-448, author = {Murea , Cornel Marius }, title = {Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {4}, pages = {448--469}, abstract = {

We present a monolithic algorithm for solving fluid-structure interaction. The Updated Lagrangian framework is used for the incompressible neo-hookean structure and Arbitrary Lagrangian Eulerian coordinate is employed for the Navier-Stokes equations. The algorithm uses a global mesh for the fluid-structure domain which is compatible with the fluid-structure interface. At each time step, a non-linear system is solved in a domain corresponding to the precedent time step. It is a semi-implicit algorithm in the sense that the velocity, the pressure are computed implicitly, but the domain is updated explicitly. Using one velocity field defined over the fluid-structure mesh, and globally continuous finite elements, the continuity of the velocity at the interface is automatically verified. The equation of the continuity of the stress at the interface does not appear in this formulation due to action and reaction principle. The stability in time is proved. A second algorithm is introduced where at each time step, only a linear system is solved in order to find the velocity and the pressure. Numerical experiments are presented.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n4.19.05}, url = {http://global-sci.org/intro/article_detail/jms/13466.html} }
TY - JOUR T1 - Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid AU - Murea , Cornel Marius JO - Journal of Mathematical Study VL - 4 SP - 448 EP - 469 PY - 2019 DA - 2019/12 SN - 52 DO - http://dor.org/10.4208/jms.v52n4.19.05 UR - https://global-sci.org/intro/article_detail/jms/13466.html KW - Fluid-structure interaction, monolithic algorithm, stability. AB -

We present a monolithic algorithm for solving fluid-structure interaction. The Updated Lagrangian framework is used for the incompressible neo-hookean structure and Arbitrary Lagrangian Eulerian coordinate is employed for the Navier-Stokes equations. The algorithm uses a global mesh for the fluid-structure domain which is compatible with the fluid-structure interface. At each time step, a non-linear system is solved in a domain corresponding to the precedent time step. It is a semi-implicit algorithm in the sense that the velocity, the pressure are computed implicitly, but the domain is updated explicitly. Using one velocity field defined over the fluid-structure mesh, and globally continuous finite elements, the continuity of the velocity at the interface is automatically verified. The equation of the continuity of the stress at the interface does not appear in this formulation due to action and reaction principle. The stability in time is proved. A second algorithm is introduced where at each time step, only a linear system is solved in order to find the velocity and the pressure. Numerical experiments are presented.

Cornel Marius Murea. (2019). Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid. Journal of Mathematical Study. 52 (4). 448-469. doi:10.4208/jms.v52n4.19.05
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