Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation

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BADRI M.A.; SABETGHADAM F.

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Journal: Modares Mechanical Engineering Year:2019 | Volume:19 | Issue:5 Page(s): 1241-1252

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Title

Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation

Author(s)

BADRI M.A. | SABETGHADAM F. | Issue Writer Certificate

Keywords

Incompressible Viscous Vorticity-Stream Function FormulationQ1

Time DilationQ1

Immersed Interface MethodQ1

Penalization FunctionsQ1

Flow Around Circular CylinderQ1

Abstract

In the present paper, a new penalization method is proposed for implementation of the rigid surfaces on the Navier-Stokes equations in the vorticity-stream function formulation. In this method, a rigid body is considered as a region in the fluid flow, where the time is stopped. Therefore, by stopping the fluid particles, this region plays the role of a rigid body. In this regard, a new transformation is introduced and applied to the governing equations and a set of modified equations are obtained. Then, in the modified equations, the Time Dilation of the solid region is approached to infinity, while the Time Dilation of the fluid region remains unit. In the article, the physical and mathematical properties of modified equations are investigated and satisfaction of the no-slip and no-penetration conditions are justified. Then, a suitable numerical algorithm is presented for solving the modified equations. In the proposed algorithm, the modified vorticity equation is time integrated via the Crank– Nicolson method, and the spatial discretization is performed with the second-order finite differencing on a uniform Cartesian grid. The method is applied to the fluid flow around a square obstacle placed in a channel, the sudden flow perpendicular to a thin flat plate, and the flow around a circular cylinder. The results show that the no-slip and no-penetration conditions are satisfied accurately, while the flow fields are also solenoidal high level of accuracy.

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APA: Copy

BADRI, M.A., & SABETGHADAM, F.. (2019). Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation. MODARES MECHANICAL ENGINEERING, 19(5 ), 1241-1252. SID. https://sid.ir/paper/178031/en

Vancouver: Copy

BADRI M.A., SABETGHADAM F.. Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation. MODARES MECHANICAL ENGINEERING[Internet]. 2019;19(5 ):1241-1252. Available from: https://sid.ir/paper/178031/en

IEEE: Copy

M.A. BADRI, and F. SABETGHADAM, “Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation,” MODARES MECHANICAL ENGINEERING, vol. 19, no. 5 , pp. 1241–1252, 2019, [Online]. Available: https://sid.ir/paper/178031/en

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