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Solving the Riemann problem at the interface gives you the values of the solution at this interface just after $t_n$. Then, the basic assumption is that this interface state remains constant during the whole time step, which is true for piece-wise constant reconstruction (i.e. the solution is assumed uniform in each cell), and as long as the CFL condition is ...


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Let me add that I've just completed a graduate certificate in Mathematics. All the math courses at NCSU teach using mostly MATLAB. I work as an engineer at LGS Labs, which used to be LGS Innovations & came from Bell Labs, has 100's of engineers that use MATLAB for prototype development of signal processing code, wireless communications modeling, and so ...


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I just found out about Voronoi particle tracking so i'm definitively not an expert. I just want to share what I have found to help others on there journey. The author of the posted Shadertoy examples has a blog where he talks about it: https://michaelmoroz.github.io/Reintegration-Tracking/ Some papers that are talking about it are not behind a paywall (...


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In case anyone is interested in the topic, we have recently proposed a FE formulation based on linearised convection operators. The advantage is that you don't need to employ an iterative strategy for solving the equations at each time step. We demonstrated first- and second-order accuracies in time, respectively, using the Backward Euler and Generalised-...


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