ABSTRACT
One of the most popular approaches that coarse-grain microscopic plasma processes is the fluid approach. In magnetized plasma this description of the plasma is often called magnetohydrodynamics. One can write the equation for both electron and ion species. Then, by summing, one obtains equations for one fluid description. Although the Lagrangian approach cures some of the problems in the Eulerian approach, it brings in its own new type of difficulties, most notably the grid entanglement as the fluid churns. Because of these numerical difficulties, as well as the cumbersome complexity of the Lagrangian algorithm, it seems instructive to start from the Eulerian approach and discuss it in detail. The Lax scheme is introduced to overcome the mentioned advective instability. The hydrodynamic particle code has its advantages in handling the non-negative density and the advective nonlinearities. Computational models can be constructed to be more efficient to follow longer time scales by reducing the original set of equations.
