nonlinear Lax-Wendroff in 2D/3D on staggered grid
In the past few years I have been developing a 3D N-S model for simulating free-surface flows (movies on http://www.math.rug.nl/~veldman/cfd-gallery.html). For the convective terms I use a first-order upwind discretisation which didn't seem to be a problem for the applications I studied. However, at the moment I'm simulating waves over a long period of time and the upwind scheme tends to be too diffusive for these problems. So I began studying flux limiter schemes based on a first-order upwind scheme in combination with a second-order Lax-Wendroff scheme. First in 1D for the linear advection equation and the nonlinear Burgers equation. This gives me very good results; far less diffusive than upwind. For the past few days I've been thinking about an extension of this method to my 3D code and this does not appear to be easy since I use a staggered (Arakawa C) grid. Has anyone been working on this? Or can you give me a reference on how to implement the Lax-Wendroff method for nonlinear advection equations in 2D/3D on a staggered grid? Thank you in advance!
Regards, Jeroen Gerrits
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