Volume 11, Issue 5
An Immersed Boundary-Simplified Gas Kinetic Scheme for 2D Incompressible Flows with Curved and Moving Boundaries

H. Dong & L. M. Yang

Adv. Appl. Math. Mech., 11 (2019), pp. 1177-1199.

Published online: 2019-06

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  • Abstract

In this work, we present an immersed boundary-simplified gas kinetic scheme for simulation of two-dimensional (2D) incompressible flows with curved and moving boundaries. Specifically, a fractional step technique with predictor and corrector processes is introduced to solve the governing equations. In the predictor step, the macroscopic governing differential equations are solved on the fixed Eulerian meshes by the recently developed simplified gas kinetic scheme (GKS). Compared to the conventional GKS, the simplified GKS is simpler and more efficient. At the same time, the simplified GKS inherits the advantage of good robustness of conventional GKS. In the corrector step, the velocity correction is carried out on the Lagrangian points by the implicit boundary condition-enforced immersed boundary method (IBM). Since it strictly originates from the no-slip boundary condition, this approach can avoid completely the unphysical streamline penetration phenomenon. Several numerical experiments show that the 2D incompressible flows with curved and moving boundaries can be well simulated by the developed scheme.

  • Keywords

Simplified GKS, immersed-boundary method, 2D incompressible flows, curved and moving boundaries.

  • AMS Subject Headings

76D17, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-1177, author = {}, title = {An Immersed Boundary-Simplified Gas Kinetic Scheme for 2D Incompressible Flows with Curved and Moving Boundaries}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {1177--1199}, abstract = {

In this work, we present an immersed boundary-simplified gas kinetic scheme for simulation of two-dimensional (2D) incompressible flows with curved and moving boundaries. Specifically, a fractional step technique with predictor and corrector processes is introduced to solve the governing equations. In the predictor step, the macroscopic governing differential equations are solved on the fixed Eulerian meshes by the recently developed simplified gas kinetic scheme (GKS). Compared to the conventional GKS, the simplified GKS is simpler and more efficient. At the same time, the simplified GKS inherits the advantage of good robustness of conventional GKS. In the corrector step, the velocity correction is carried out on the Lagrangian points by the implicit boundary condition-enforced immersed boundary method (IBM). Since it strictly originates from the no-slip boundary condition, this approach can avoid completely the unphysical streamline penetration phenomenon. Several numerical experiments show that the 2D incompressible flows with curved and moving boundaries can be well simulated by the developed scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0244}, url = {http://global-sci.org/intro/article_detail/aamm/13206.html} }
TY - JOUR T1 - An Immersed Boundary-Simplified Gas Kinetic Scheme for 2D Incompressible Flows with Curved and Moving Boundaries JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1177 EP - 1199 PY - 2019 DA - 2019/06 SN - 11 DO - http://dor.org/10.4208/aamm.OA-2018-0244 UR - https://global-sci.org/intro/article_detail/aamm/13206.html KW - Simplified GKS, immersed-boundary method, 2D incompressible flows, curved and moving boundaries. AB -

In this work, we present an immersed boundary-simplified gas kinetic scheme for simulation of two-dimensional (2D) incompressible flows with curved and moving boundaries. Specifically, a fractional step technique with predictor and corrector processes is introduced to solve the governing equations. In the predictor step, the macroscopic governing differential equations are solved on the fixed Eulerian meshes by the recently developed simplified gas kinetic scheme (GKS). Compared to the conventional GKS, the simplified GKS is simpler and more efficient. At the same time, the simplified GKS inherits the advantage of good robustness of conventional GKS. In the corrector step, the velocity correction is carried out on the Lagrangian points by the implicit boundary condition-enforced immersed boundary method (IBM). Since it strictly originates from the no-slip boundary condition, this approach can avoid completely the unphysical streamline penetration phenomenon. Several numerical experiments show that the 2D incompressible flows with curved and moving boundaries can be well simulated by the developed scheme.

H. Dong & L. M. Yang. (2019). An Immersed Boundary-Simplified Gas Kinetic Scheme for 2D Incompressible Flows with Curved and Moving Boundaries. Advances in Applied Mathematics and Mechanics. 11 (5). 1177-1199. doi:10.4208/aamm.OA-2018-0244
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