In standard grid-based approaches to solving hydrodynamical problems, a volume of space is subdivided into finite-sized cells, and the physical quantities such as temperature, density, fluid velocity, etc., are computed inside those cells or at cell faces using finite difference or finite volume techniques as discussed above (see, e.g., Bodenheimer.
Shocks are discontinuities in the flow of the fluid. A shock front is a surface that is characterized by a nearly discontinuous change inP, ρ, v ⊥, and T, where v ⊥ is the component of the velocity perpendicular to the shock front. Related to shocks but generally less problematic to simulate are contact discontinuities. A contact discontinuity is c.
The second approach to handling shocks is to implement an artificial viscosity. Shocks are nearly discontinuous physically, with a characteristic width of a few particle mean free paths. This in general is many times smaller than the typical grid spacing in simulations. By introducing an artificial viscosity, the shock front may be artificially spr.
The challenges of numerical methods in astrophysics are due to their huge range of scales
This warrants extremely robust numerical methods
Examples are very low densities, which numerically are not allowed to deviate below zero, or shocks at very high Mach numbers that need to be computed in stable manner
Numerical simulations in an astrophysical context usually model initial value and/or boundary value problems
If the former, we follow the state of a system evolved through time, and if the alter, the equations describing the system at a given point in time are solved (Bodenheimer et al
,2007 )Currently and for the foreseeable future, numerical astrophysics is an indispensable means of studying the evolution universe and its contents
Here will be presented a brief overview of the numerical techniques most commonly used to model astrophysical objects and phenomena
