Finite difference representations of vorticity transport (Q794513)

The numerical diffusion of the vorticity transport in computation of viscous flow is very important, as it affects the numerical accuracy of the solution of fluid dynamics. The author summarizes the most commonly used explicit finite difference representations of the two-dimensional Navier-Stokes equations, such as central difference and upwind difference approximations, second-order approximation according to \textit{D. G. Briggs} [ibid. 6, 233--241 (1975; Zbl 0308.76058)], approximation according to \textit{D. N. de G. Allen} and \textit{R. V. Southwell} [Q. J. Mech. Appl. Math. 8, 129--145 (1955; Zbl 0064.19802)] and second-order diffusion approximation. The author also analyzes the matrix diagonally dominant with numerical diffusion and local truncation error of the boundary layer for the vorticity. This paper is available to those beginners who want to learn and use the numerical technique for computing viscous flow problem, but they should read more concerned references, if they want to understand further how to estimating the numerical diffusion error.