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To: 1.3.5 Diffusion velocity method |
A method with properties similar to the particle strength exchange (PSE)
scheme was derived by Fishelov [78].
She convolves the spatial derivatives in the vorticity equation
with a smoothing function and then transfers
the derivatives on to that function. This procedure of using
smoothing functions to compute spatial derivatives is similar to
the procedure used in the Smoothed Particle Hydrodynamics (SPH) method
[22,25,88,140,157,158].
Fishelov showed that the 
norm of the vorticity
does not increase in her method, implying stability, at least for the heat
equation, provided that the Fourier transform of the smoothing function is
nonnegative. This method readily extends to higher order of accuracy.
With proper discretization, it can be made to conserve vorticity
exactly. Recently, Bernard & Thomas [23,24]
have applied this method to boundary layers over flat plates.
However, Fishelov's method requires periodic remeshing and particle overlap to maintain accuracy [23,24] like the PSE scheme. It has therefore similar disadvantages.