Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n ≪ 1, and solutions of the relevant differential equations are obtained analytically, to the second order of n. Some solved and unsolved problems of polytropic models ...

Copyright q 2012 J. Yang and Z. Zhuang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We rigorously justify a singular Euler-Poisson approximation of the incompressible Euler equations in the quasi-neutral regime for plasma phys...

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal with the incompressibility constraint. The stability of the scheme has been proven in [15]. We infer from it its convergence. Mathematics Subject ...

We present a novel boundary handling scheme for incompressible fluids based on Smoothed Particle Hydrodynamics (SPH). In combination with the predictive-corrective incompressible SPH (PCISPH) method, the boundary handling scheme allows for larger time steps compared to existing solutions. Furthermore, an adaptive time-stepping approach is proposed. The approach automatically estimates appropria...

In the present paper we provide the decomposition and local estimates for the pressure function for the non-stationary flow of incompressible non-Newtonian fluids in Orlicz spaces. We show that this method can be applied to prove the existence of weak solutions to the problem of motion of one or several rigid bodies in a non-Newtonian incompressible fluid with growth conditions given by an N -f...

We provide local formulas for the pressure of incompressible fluids. The pressure can be expressed in terms of its average and averages of squares of velocity increments in arbitrary small neighborhoods. As application, we give a brief proof of the fact that C velocities have C (or Lipschitz) pressures. We also give some regularity criteria for 3D incompressible Navier-Stokes equations. Dedicat...

The presence of even a small amount of surfactant at the particle-laden fluid interface subjected to shear makes surface flow incompressible if the shear rate is small enough [T. M. Fischer et al., J. Fluid Mech. 558, 451 (2006)]. In the present paper the effective surface shear viscosity of a flat, low-concentration, particle-laden incompressible interface separating two immiscible fluids is c...

We show that at zero temperature the Coulomb drag between two layers of Landau level filling factor ν = 1/2 is finite in the incompressible paired quantum Hall liquid limit. The temperature dependence of the Coulomb drag exhibits a minimum near the temperature where the transition between the incompressible double layer quantum Hall liquid state and the weakly coupled compressible state takes p...

In incompressible flows with vanishing normal velocities at the boundary, irrotational forces in the momentum equations should be balanced completely by the pressure gradient. Unfortunately, nearly all available discretization methods for incompressible flows violate this property. The origin of the problem is that discrete velocity approximations of incompressible flows are usually not diverge...

The smoothed particle hydrodynamics method has been deeply studied and validated for the past decades on a weakly-compressible fluid discretization for the Euler equations. Recently several authors have proposed the use of SPH truly-incompressible algorithms in the most varied domains of computational fluid dynamics. Within this technique, based on the projection method, a pressure Poisson equa...