2.3.5 Discretization in space: grids
In one spatial dimension one can choose between

Eulerian grid: fixed in space

Lagrangian grid: moving with the flow (makes the linear 1D advection trivial)
 Hybrid grid: moving with another speed
 No ``grid'': SPH (grid is replaced by particle positions)
In the following examples the grid points will be fixed (Eulerian) and equidistant.
 In multidimensions things become more complicated.
 Some advanced ``real world'' techniques
(hierarchical grids perhaps with adaptive mesh refinement)
are build upon methods with simple Eulerian grids.