Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first applied in Newtonian hydrodynamics, provides a robust methodology to obtain stable and accurate solutions even in the presence of discontinuities. The knowledge...

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analogue of BenjaminOno equation. The latter is known to describe internal waves o...

Statement of problem on vortical inviscid flow of barotropic and incompressible fluids. Abstract The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the f...

In this work, the results are presented of a 3D numerical magneto-hydrodynamic (MHD) simulation of direct current (DC) electromagnetic pump for liquid aluminum at large Reynolds number under externally imposed non-uniform magnetic field. The formulation of the magneto hydrodynamic model has been derived from the Reynolds-Averaged NavierStokes equations with standard k-ε turbulence model coupled...

The evolution to the steady state of a granular gas subject to simple shear flow is analyzed by means of computer simulations. It is found that, regardless of its initial preparation, the system reaches (after a transient period lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic regime, even at strong dissipation and for states where the time scale associated with in...

The obstructions to the existence of a hierarchy of hydrodynamic conservation laws are studied for a multicomponent dispersionless KdV system. It is shown that if an underlying algebra is Jordan, then the lowest obstruction vanishes and that all higher obstructions automatically vanish. Deformations of these multicomponent dispersionless KdV-type equations are also studied. No new obstructions ...

In this work, rising of a single bubble in a quiescent liquid under microgravity condition was simulated. The related unsteady incompressible full Navier-Stokes equations were solved using a conventional finite difference method with a structured staggered grid. The interface was tracked explicitly by connected marker points via hybrid front capturing and tracking method. One field approximatio...