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Non-local aggregation-diffusion equations are used to describe large groups of particles at the macro scale. In particular, these equations are used to model a biological system of interacting species involving dispersal, drift, and non-local interactions. The existence and uniqueness of solution to these degenerate Parabolic Partial Differential Equations are well known in literature. I will present the construction of a time continuous Finite Volume Scheme that preserves the structural properties of the equations such as energy dissipation and non-negativity of density, discretized on general meshes in any dimension. Convergence results for the scheme, hinges on a concept called Compensated Compactness, which will be presented as a modification to the famous Aubin-Lions Lemma. Finally, we will look at a few interesting insights into implementation of the scheme and parallelization on HPC infrastructure.
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