Finite Element Solution of the 3D Compressible Navier-Stokes Equations by a Velocity-Vorticity Method

A 3D incompressible Navier–Stokes velocity–vorticity weak form finite element algorithm

“…For Re = 100, this uvelocity component data reported by Ku et al [18], Guj and Stella [10], Fujima et al [19], and Jiang et al [21] agree quite well with each other. The computed solution from the present formulation is shown in Figure 7.…”

“…The vorticity boundary condition at a no-slip wall was imposed by evaluating the weighted area integral of the kinematic deÿnition of vorticity in terms of velocity in each boundary element. Three dimensional viscous ow solutions for driven cavity ow at Re = 100 and Re = 400 were also reported [10].…”

Vortex particle-in-cell method for three-dimensional viscous unbounded flow computations

“…For velocity-vorticity formulations, several studies have appeared in the literature, e.g. Dacles and Hafez [1], Fasel [14], Dennis et al [15], Farouk and Fusegi [16], Napolitano and Pascazio [17], Daube [18], Ern and Smooke [19], Guj and Stella [20], and Guevremont and Habashi [21]. Given an initial distribution of vorticity, the evolution of the velocity and vorticity may be computed by solving Equations (2) and (3) subjected to appropriate boundary conditions.…”

Velocity–vorticity–helicity formulation and a solver for the Navier–Stokes equations

“…It was already mentioned in the introduction that correctly determining and implementing vorticity boundary conditions, especially at a no-slip -no-penetration wall, is important. In our implementation we use the projection of the kinematic definition of vorticity, see step 2 of Algorithm 4.1, as was first suggested in [17,18]. We note that the accuracy of the vorticity boundary condition at a no-slip wall can be increased to the second order by using more sophisticated approach based nodal velocity expansions in the nearboundary nodes as suggested in [33].…”