Abstract
A novel method of integrating solenoidal flows given on a grid is developed. In three dimensions, the method involves splitting the flow into two or possibly three flows that are two dimensional and area preserving, and can therefore be integrated by Crank–Nicolson or a modified form of leapfrog, both of which exactly conserve area. The method involves an interpolation scheme which ensures the solenoidal nature of the field throughout the domain (on and off the grid) by means of tricubic splines. It is shown that the method is easily generalized to arbitrary curvilinear coordinates and also generalizes to higher dimensions. A method of integrating compressional three-dimensional flows given on a grid is outlined.
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