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 multi-dimensions things become more complicated.
• Some advanced ``real world'' techniques (hierarchical grids perhaps with adaptive mesh refinement) are build upon methods with simple Eulerian grids.