Area preservation in computational fluid dynamics

Details Area preservation in computational fluid dynamics Area preservation in computational fluid dynamics

1999-07-05

arxiv.org/abs/math/9907025v1

Mathematics

Numerical Analysis

14 pages incl. 3 figures

Scientific paper

10.1016/S0375-9601(99)00763-X

Incompressible two-dimensional flows such as the advection (Liouville) equation and the Euler equations have a large family of conservation laws related to conservation of area. We present two Eulerian numerical methods which preserve a discrete analog of area. The first is a fully discrete model based on a rearrangement of cells; the second is more conventional, but still preserves the area within each contour of the vorticity field. Initial tests indicate that both methods suppress the formation of spurious oscillations in the field.

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