Abstract. The procedure of solving the system of the Navier-Stokes equations is proposed. The initial conditions: the velocity divergence (dilatation) being zero and the temperature being the known function, the initial density being constant. The problem is set in the infinite space. The solution of the Navier-Stokes equations was reduced to the solution of integral equations of the Volterra t...

The immersed boundary method is an algorithm for simulating the interaction of immersed elastic bodies or boundaries with a viscous incompressible fluid. The immersed elastic material is represented in the fluid equations by a system or field of applied forces. The particular case of Stokes flow with applied forces on a periodic domain involves two related mathematical complications. One of the...

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes’ problems. Traditionally, exact solutions to the Stokes’ problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and...

The phenomenon of stimulated Raman scattering (SRS) can be described by three coupled PDEs which define the pump electric field, the Stokes electric field, and the material excitation as functions of distance and time. In the transient limit these equations are integrable, i.e., they admit a Lax pair formulation. Here we study this transient limit. The relevant physical problem can be formulate...

The third problem for the Stokes system is studied on a bounded domain in R with Ljapunov connected boundary. We construct a solution of this problem in the form of appropriate potentials and determine unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in the form of a series. Then we study the integral equation which we obtain...

measuring field gravity in sea due to the accelerations introduced via waves and movements to the gravity measuring systems has a low accuracy since according to einstein's equalent principle, gravimeter isn't able to separate the gravity acceleration from another acceleration. ship borne gravimetery observations by means of like oscillations and accelerations of the ship motion, and ...

We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible flows. The discretization of the Navier-Stokes operator is done using boundary integrals and structured-grid finite elements. We use finite-differences to advance the equations in time. The convecti...

We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. This work extends the theory introduced in a previous paper (Al-Malki et al. 1999) in which scattering polarization from a spherically symmetric envelope illuminated by an anisotropic point source was considered. Here we generalize to account for the more realistic expectation of a n...

We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible laminar flows. The Navier-Stokes operator discretization is done using boundary integrals and structured-grid finite elements. We use a two-step second-order accurate scheme to advance the equations...