(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am using the boundary element method to solve unknowns to the Laplace equation from classic potential flow theory for the time evolution of a fluid air interface. At each time step, I need to solve a material derivative equation numerically at every node along an interface to find the new velocity potential.

In order to calculate the material derivative, I need to calculate the local interface curvature (et al.).

2. Relevant equations

From text, the local (mean) interface curvature can be calculated as 2H=div n. Where H is the mean interface curvature and n is the unit normal to the surface.

3. The attempt at a solution

The divergence of a vector field is a somewhat trivial calculation, e.g.:

div F = (dF1/dx+dF2/dy+dF3/z) where each value of F is some function that can be differentiated (pde) (like x*y^2). So here is the problem/question, in the case of the unit normal, the values are scalar values (such as [1 0 1]'), therefore if I differentiate each of these values with respect to the independent variable the entire equation equals zero. No doubt I am missing something fundamental here, any advise would be greatly appreciated.

I've attached a very simple sketch of a local discretized interface with nodes, and a unit normal just to help visualize what I am working with.

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# Homework Help: Local Interface Curvature

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