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Level Set Numerical Surface Tension Calculation

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Old   November 5, 2011, 00:33
Default Level Set Numerical Surface Tension Calculation
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Michael Franklin
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Given a phase-function 0<phi(x,y)<1 that varies smoothly from 0 to 1 in a narrow region (approx. 6 grid cells from 0.05<phi<0.95), the gradients are:


which are approximated via central difference. This value is located at a grid cell center (i,j) due to central difference formula. The normal vector field is then approximated as

N = gradient/mag(gradient)

This is also located at cell center (i,j). The curvature is the divergence of normal vectors, i.e.

kappa = div(normal)

also located at cell center (i,j). Now...for the surface tension, whose x and y components are located at right edges (i+1/2,j) and top edges (i,j+1/2), respectively...

When I plot gradients, normals, and curvatures, they are all symmetric, i.e., around a circle, all values point perfectly radially outward (normal) to the level set phi=0.5 interface, but when I plot my surface tension, it appears to be asymmetric! I have even taken care to stagger these two vector fields (that are located at different spatial points, remember!) when I plot the field.

Does anybody have any advice? The surface tension (presented in the paper who's work I'm following, Olsson & Kreiss, "A conservative level set method for two phase flow") is a forward difference calculation, whereas normal and gradient calculations are central differences. I'm following their method EXACTLY, I've checked everything...and yet, asymmetric surface! is offline   Reply With Quote


gradients, level set method, normals, phase field, surface tension

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