Volume 17, Issue 2

- We numerically analyse the momentumless turbulent wake evolution in a linearly stratified medium, using two mathematical models. The computational results are compared with experimental data. We consider the model, which satisfactorily describes the process of anisotropy turbulence decay in the wake, taking into account the buoyancy effect in the algebraic model of third-order correlations in the velocity field.

- Using momentum balance equations and kinetic turbulent energy equations, we study plane turbulent wake dynamics in an incompressible fluid. We construct for a fluid flow in the far wake the self-similar solution to the problem, prove that the model studied is well-posed. We study the qualitative properties of solutions and their asymptotic behaviour.

- In this paper we give the results on the calculation of the wave motion of a fluid on adaptive grids when a solitary wave runs up at a stationary rectangular body which is partially immersed in a fluid and is not in contact with the bottom. We study the effect of the length and immersion of a body and the amplitude of an incident wave on a maximum wave run-up, the wave pattern in front of and behind a body, force action on a body. Numerical algorithms are based on a one-dimensional nonlinear shallow-water model and a nonlinear model of potential plane flows of an ideal incompressible fluid. We compare the computational results obtained by various models with the experimental data in [9].

- To effectively solve the Euler equations in integral form, which are approximated by the finite volume method, we use splitting approach developed earlier for the solution of aerohyrodynamics problems. The constructed algorithms have a property of minimum dissipation and are efficient.

- The paper formulates a comprehensive grid generator based on the Beltramian operator. For the purpose of control of the grid quality the necessary relations between the curvatures of the boundary segments of monitor surfaces and the behaviour of the grid lines near the boundaries of these surfaces are established

- We study difference schemes with indefinite coefficients and indefinite right-hand sides on stencils that consist of any number of arbitrarily located points. In the two-dimensional case we obtain linear systems of equations for the calculation of coefficients in ordinary (noncompact) and compact schemes and conditions on the right-hand side under which the approximation order of differential equations would be equal to a predetrmined natural number. Analogously we study the behaviour of ordinary and compact approximations of universal boundary conditions, including the conditions of the first, second, and third kinds. In the three-dimensional case we establish the number of conditions which specify coefficients and the right-hand sides of schemes. We consider particular examples of schemes in the plane and in the space.