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This statement seems a bit reductive for what is a rather large and involved problem. But multigrid, although it was developed for and is ideal for elliptic problems, is still just about the best we have for hyperbolic problems and sees widespread use (when people can manage to implement it). The comparison between Gauss-Seidel seems odd as they tend to ...

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This is probably too late to help you, but here is a compact code that will do points, weights and first derivatives for Gauss, Lobatto or either Radau. function [x,w,A] = OCnonsymGLReig(n,meth) % code for nonsymmetric orthogonal collocation applications on 0 < x < 1 % n - interior points % meth = 1,2,3,4 for Gauss, Lobatto, Radau (right), ...

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Based on the image that you provided in your comment, I believe you formulate your problem as a system of PDEs for each branch in your network and make sure at each connecting node mass is conserved. Let's say you have $N$ branches, so you need to solve the system of advection-diffusion equations for each branch ($1 \leqslant i \leqslant N$): \frac{\...

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I disagree with the answer given by Alone Programmer. His reasoning is not objective and seems to be based on a very primitive lattice-Boltzmann model with BGK collision operator. LBM has significantly matured over the years and is in my opinion a very attractive numerical solver. Nonetheless it depends on the application if it really fits your needs. I ...

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