Solving Laplace equation with nonlinear diffusity/conductivity -- CFD Online Discussion Forums

October 20, 2014, 06:40	Solving Laplace equation with nonlinear diffusity/conductivity	#1
chriss85 Senior Member Join Date: Oct 2013 Posts: 397 Rep Power: 18	I want to solve a Laplace equation, div(sigma * grad(phi)) = 0, where sigma depends nonlinearly on the solution of phi. What is the best approach for doing something like this? If I solve the equation iteratively and update sigma each time based on the current solution, what kind of conditions are required to guarantee convergence and unique solutions? Is it possible (and beneficial) to perform this kind of iteration directly in the matrix solver?

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