Regular ArticleEffective Vorticity-Velocity Formulations for Three-Dimensional Incompressible Viscous Flows
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Parallel implementation of a VIScous Vorticity Equation (VISVE) method in 3-D laminar flow
2021, Journal of Computational PhysicsCitation Excerpt :Depending on whether the velocity or the stream–function is involved in the equations, the methods are further classified into the vorticity–velocity formulations [30–33] and the vorticity–stream–function formulations [34,35,1]. The Finite Difference Methods (FDM) were commonly used to discretize the governing equations, yet the FDM shows considerable difficulties in handling non–orthogonal grids, and so the above applications were limited to flow in simple and regular computational domains, such as a rectangular domain [30,32–34,1] or a cylindrical domain [31]. Even though Elshabka and Chung [35] proposed a Finite Element Method (FEM) scheme to solve the 3–D vorticity transport equation, the results presented were still about the 3–D cavity flow in a rectangular domain.
A conservative viscous vorticity method for unsteady unidirectional and oscillatory flow past a circular cylinder
2019, Ocean EngineeringCitation Excerpt :Whether the velocity or the stream function is used to represent the kinematics of the flow further categorizes these methods into the vorticity–velocity formulation and the vorticity-stream function formulation. The velocity field and the vorticity field are usually associated by a Poisson equation (Wu et al., 1995). Remarkably, Wu and Thompson (1973) proposed an integro-differential scheme that enables calculating the velocity by a direct and explicit integral of the vorticity.
Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations
2019, Journal of Differential EquationsVorticity vector-potential method for 3D viscous incompressible flows in time-dependent curvilinear coordinates
2016, Journal of Computational PhysicsCitation Excerpt :A variety of numerical methods based on vorticity–velocity formulation have been developed. To enforce the solenoidal conditions properly, the vorticity was projected into the divergence-free space in [9]. Also, staggered grids have been widely used in the vorticity–velocity formulation to overcome numerical difficulties ever since the pioneering work of Harlow and Welch on MAC scheme [10].
Natural vorticity boundary conditions on solid walls
2015, Computer Methods in Applied Mechanics and EngineeringA new velocity-vorticity formulation for direct numerical simulation of 3D transitional and turbulent flows
2015, Journal of Computational Physics