Is relativistic hydrodynamics always symmetric-hyperbolic in the linear regime?

Is standard symmetric formulation always better for smoothed particle hydrodynamics?

We try to demonstrate in this article that, for quasi-incompressible flows, the standard symmetric formulation of pressure gradient in smoothed particle hydrodynamics (SPH) is not necessarily superior to asymmetric ones. Comparative simulations on plane Poiseuille flows at very low Reynolds numbers show that the results using symmetric formulation are more dependent on the computational sound s...

General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics

Simple solutions of relativistic hydrodynamics for cylindrically symmetric systems

Simple, self-similar, analytic solutions of 1 + 3 dimensional relativistic hydrodynamics are presented for cylindrically symmetric fireballs corresponding to central collisions of heavy ions at relativistic bombarding energies.

Special relativistic spherically symmetric Lagrangean hydrodynamics from General Relativity

We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is, for the case of weak gravitational fields. Explicit formulae are presented which relate General Relativistic independent variables, Lagrangean mass coordina...

Exploring the relativistic regime with Newtonian hydrodynamics: II. An effective gravitational potential for rapid rotation

We present the generalization of a recently introduced modified gravitational potential for selfgravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian hydrodynamics code also in cases of rapid rotation. We test this approach in numerical simulations of astrophysical scenarios related to compact stars, like sup...