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This lecture covers numerical methods in hydrodynamics, focusing on the simulation of ideal fluids and the plasma universe. Topics include Eulerian vs. Lagrangian methods, discretization, hydrodynamical PDEs, and analytical solutions. The lecture also delves into the simulation of dark matter and baryons, as well as the modeling of extra baryonic subgrid physics. Various integration schemes and simulation projects like Aquarius, Auriga, and NIHAO are discussed.