Volume 13, Issue 1
A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary

Jingyang Wang & Chunhua Zhou

Adv. Appl. Math. Mech., 13 (2021), pp. 83-100.

Published online: 2020-10

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  • Abstract

In this paper, a novel immersed boundary method is presented for simulating incompressible flows governed by Navier-Stokes equations. A virtual boundary is formed by the cell edges (for two-dimensional cases) in the vicinity of the immersed boundary. In the domain with the virtual boundary, the governing equations can be solved in the conventional way. Reconstructed velocity is imposed on the virtual boundary, which is determined via the interpolation along the direction normal to the wall and in conjunction with the no-slip condition for the actual boundary. For "freshly cleared nodes" on the virtual boundary encountered in moving-boundary problems, pressure at the previous time step is reconstructed by solving the local simplified momentum equation. In the test case for an analytical solution, the local accuracy of pressure is verified to be of the second order. In order to further validate the present method, various flows over the stationary and/or moving circular cylinder and NACA0012 airfoil have been simulated. The obtained results agree well with the available numerical or experimental data in the published literatures.

  • Keywords

Immersed boundary method, boundary condition, convergence rate, solution reconstruction.

  • AMS Subject Headings

76D05, 76M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-83, author = {Jingyang Wang , and Chunhua Zhou , }, title = {A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {1}, pages = {83--100}, abstract = {

In this paper, a novel immersed boundary method is presented for simulating incompressible flows governed by Navier-Stokes equations. A virtual boundary is formed by the cell edges (for two-dimensional cases) in the vicinity of the immersed boundary. In the domain with the virtual boundary, the governing equations can be solved in the conventional way. Reconstructed velocity is imposed on the virtual boundary, which is determined via the interpolation along the direction normal to the wall and in conjunction with the no-slip condition for the actual boundary. For "freshly cleared nodes" on the virtual boundary encountered in moving-boundary problems, pressure at the previous time step is reconstructed by solving the local simplified momentum equation. In the test case for an analytical solution, the local accuracy of pressure is verified to be of the second order. In order to further validate the present method, various flows over the stationary and/or moving circular cylinder and NACA0012 airfoil have been simulated. The obtained results agree well with the available numerical or experimental data in the published literatures.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0354}, url = {http://global-sci.org/intro/article_detail/aamm/18341.html} }
TY - JOUR T1 - A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary AU - Jingyang Wang , AU - Chunhua Zhou , JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 83 EP - 100 PY - 2020 DA - 2020/10 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0354 UR - https://global-sci.org/intro/article_detail/aamm/18341.html KW - Immersed boundary method, boundary condition, convergence rate, solution reconstruction. AB -

In this paper, a novel immersed boundary method is presented for simulating incompressible flows governed by Navier-Stokes equations. A virtual boundary is formed by the cell edges (for two-dimensional cases) in the vicinity of the immersed boundary. In the domain with the virtual boundary, the governing equations can be solved in the conventional way. Reconstructed velocity is imposed on the virtual boundary, which is determined via the interpolation along the direction normal to the wall and in conjunction with the no-slip condition for the actual boundary. For "freshly cleared nodes" on the virtual boundary encountered in moving-boundary problems, pressure at the previous time step is reconstructed by solving the local simplified momentum equation. In the test case for an analytical solution, the local accuracy of pressure is verified to be of the second order. In order to further validate the present method, various flows over the stationary and/or moving circular cylinder and NACA0012 airfoil have been simulated. The obtained results agree well with the available numerical or experimental data in the published literatures.

Jingyang Wang & Chunhua Zhou. (2020). A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary. Advances in Applied Mathematics and Mechanics. 13 (1). 83-100. doi:10.4208/aamm.OA-2019-0354
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