Abstract
This chapter refers to two different ways of deriving schemes for the smoothed particle hydrodynamics method. The first is based on Newtonian mechanics, while the second on Lagrangian mechanics. It becomes obvious that in order to extend smoothed particle hydrodynamics to fully compressible processes, the latter approach is necessary. Additionally, this chapter focuses on a core algorithm for fully compressible schemes: the neighbors search using a kd-tree search.
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