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	Finite volume solution of the Navier-Stokes equations in velocity-vorticity formulation
	Zhu, BS
	2010-05-11 ; 2010-05-11
关键词	velocity-vorticity formulation finite volume integral formulae fractional step method vorticity boundary conditions VORTEX METHODS FLOW IMPLEMENTATION CYLINDER Computer Science, Interdisciplinary Applications Mathematics, Interdisciplinary Applications Mechanics Physics, Fluids & Plasmas
中文摘要	For the incompressible Navier-Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity-pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity-vorticity integro-differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot-Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-flow and no tangential-flow boundary conditions. We impose a no-flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd.
语种	英语 ; 英语
出版者	JOHN WILEY & SONS LTD ; CHICHESTER ; THE ATRIUM, SOUTHERN GATE, CHICHESTER PO19 8SQ, W SUSSEX, ENGLAND
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/25943]
专题	清华大学
推荐引用方式 GB/T 7714	Zhu, BS. Finite volume solution of the Navier-Stokes equations in velocity-vorticity formulation[J],2010, 2010.
APA	Zhu, BS.(2010).Finite volume solution of the Navier-Stokes equations in velocity-vorticity formulation..
MLA	Zhu, BS."Finite volume solution of the Navier-Stokes equations in velocity-vorticity formulation".(2010).

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