The turn function and vorticity method for numerical fluid dynamics

A numerical method is presented that solves in a consistent fashion, conservation equations for both vorticity and linear momentum in multidimensional fluid-dynamics calculations. The equations are given in both two- and three-dimensional Cartesian geometry, and it is shown how the method can be easily implemented in a two-dimensional Eulerian fluid-dynamics code. The results of example calculations, which were performed with and without the new method, show the large errors that can arise when the vorticity equation is not solved in compressible flow calculations.