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Volume 12, Issue 2
A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies

Junjie Wang, Yadong Li, Jie Wu & Fusheng Qiu

Adv. Appl. Math. Mech., 12 (2020), pp. 545-563.

Published online: 2020-01

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  • Abstract

In this paper, a variable correction-based immersed boundary method (IBM) for simulating viscous compressible flows over stationary and moving bodies is presented. It is the extension of the implicit velocity correction-based IBM proposed by Wu and Shu (J. Comput. Phys., 228 (2009), pp.  1963-1979). Since the incompressible flow was studied in their work, only the fluid velocity field was needed to be corrected by enforcing the no-slip boundary condition. But for compressible flow problems, other flow variables around the boundary also should be corrected or updated. To simulate the flow field without the effect of immersed boundary firstly, the open source code OpenFOAM is utilized in this work. After performing the velocity correction then, the density is corrected by resolving the continuity equation with the corrected fluid velocity. After that, the temperature surrounding the boundary is corrected from the given temperature condition, which is similar to the velocity correction. Finally, the pressure is updated by using the corrected density and temperature through the equation of state. In such way, all the flow variables have been corrected and the given physical boundary conditions can be accurately implemented. To validate the proposed method, the flows over a stationary circular cylinder, a stationary airfoil and a transversely oscillating circular cylinder at different Mach and Reynolds numbers are simulated. Compared to the results in the literature, good agreement can be achieved. To further illustrate the potential of current method for dealing with complex problems, the flow over a rotating cylinder in front of a stationary cylinder is also simulated.

  • AMS Subject Headings

68U20, 76D17, 76N99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wuj@nuaa.edu.cn (Jie Wu)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-545, author = {Wang , JunjieLi , YadongWu , Jie and Qiu , Fusheng}, title = {A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {545--563}, abstract = {

In this paper, a variable correction-based immersed boundary method (IBM) for simulating viscous compressible flows over stationary and moving bodies is presented. It is the extension of the implicit velocity correction-based IBM proposed by Wu and Shu (J. Comput. Phys., 228 (2009), pp.  1963-1979). Since the incompressible flow was studied in their work, only the fluid velocity field was needed to be corrected by enforcing the no-slip boundary condition. But for compressible flow problems, other flow variables around the boundary also should be corrected or updated. To simulate the flow field without the effect of immersed boundary firstly, the open source code OpenFOAM is utilized in this work. After performing the velocity correction then, the density is corrected by resolving the continuity equation with the corrected fluid velocity. After that, the temperature surrounding the boundary is corrected from the given temperature condition, which is similar to the velocity correction. Finally, the pressure is updated by using the corrected density and temperature through the equation of state. In such way, all the flow variables have been corrected and the given physical boundary conditions can be accurately implemented. To validate the proposed method, the flows over a stationary circular cylinder, a stationary airfoil and a transversely oscillating circular cylinder at different Mach and Reynolds numbers are simulated. Compared to the results in the literature, good agreement can be achieved. To further illustrate the potential of current method for dealing with complex problems, the flow over a rotating cylinder in front of a stationary cylinder is also simulated.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0015}, url = {http://global-sci.org/intro/article_detail/aamm/13633.html} }
TY - JOUR T1 - A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies AU - Wang , Junjie AU - Li , Yadong AU - Wu , Jie AU - Qiu , Fusheng JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 545 EP - 563 PY - 2020 DA - 2020/01 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0015 UR - https://global-sci.org/intro/article_detail/aamm/13633.html KW - Immersed boundary method, compressible flows, variable correction, stationary and moving bodies, OpenFOAM. AB -

In this paper, a variable correction-based immersed boundary method (IBM) for simulating viscous compressible flows over stationary and moving bodies is presented. It is the extension of the implicit velocity correction-based IBM proposed by Wu and Shu (J. Comput. Phys., 228 (2009), pp.  1963-1979). Since the incompressible flow was studied in their work, only the fluid velocity field was needed to be corrected by enforcing the no-slip boundary condition. But for compressible flow problems, other flow variables around the boundary also should be corrected or updated. To simulate the flow field without the effect of immersed boundary firstly, the open source code OpenFOAM is utilized in this work. After performing the velocity correction then, the density is corrected by resolving the continuity equation with the corrected fluid velocity. After that, the temperature surrounding the boundary is corrected from the given temperature condition, which is similar to the velocity correction. Finally, the pressure is updated by using the corrected density and temperature through the equation of state. In such way, all the flow variables have been corrected and the given physical boundary conditions can be accurately implemented. To validate the proposed method, the flows over a stationary circular cylinder, a stationary airfoil and a transversely oscillating circular cylinder at different Mach and Reynolds numbers are simulated. Compared to the results in the literature, good agreement can be achieved. To further illustrate the potential of current method for dealing with complex problems, the flow over a rotating cylinder in front of a stationary cylinder is also simulated.

Junjie Wang, Yadong Li, Jie Wu & Fusheng Qiu. (2020). A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies. Advances in Applied Mathematics and Mechanics. 12 (2). 545-563. doi:10.4208/aamm.OA-2019-0015
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