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Abstract: The paper presents a detailed review of the smooth particle hydrodynamicsSPH method with particular focus on its astrophysical applications. We startby introducing the basic ideas and concepts and thereby outline all ingredientsthat are necessary for a practical implementation of the method in a workingSPH code. Much of SPH-s success relies on its excellent conservation propertiesand therefore the numerical conservation of physical invariants receives muchattention throughout this review. The self-consistent derivation of the SPHequations from the Lagrangian of an ideal fluid is the common theme of theremainder of the text. We derive a modern, Newtonian SPH formulation from theLagrangian of an ideal fluid. It accounts for changes of the local resolutionlengths which result in corrective, so-called -grad-h-terms-. We extend thisstrategy to special relativity for which we derive the corresponding grad-hequation set. The variational approach is further applied to ageneral-relativistic fluid evolving in a fixed, curved background space-time.Particular care is taken to explicitely derive all relevant equations in acoherent way.



Author: Stephan Rosswog

Source: https://arxiv.org/



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