Many numerical techniques have been developed to solve the hydrodynamic and collisionless particle equations in this limit. For the hydrodynamic equations, the methods range from Eulerian finite difference techniques [8, 18, 56] to unstructured particle methods [29, 34]. For the collisionless particle or dark matter equations, the canonical choices are treecodes or PM and P M methods , although many variants have been developed to optimize computational performance and accuracy, including grid and particle refinement methods. The reader is referred to  for a comparison of several different numerical methods applied to a common problem of structure formation. A method for solving non-equilibrium, multi-species chemical reaction flows together with the hydrodynamic equations in a background FLRW model is described in [1, 9].
|Physical and Relativistic Numerical Cosmology
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