2D shallow water equations with depth-averaged k−ε model is considered. A meshless method based on multiquadric radial basis functions is described. This methods is based on the collocation formulation and does not require the generation of a grid and any integral evaluation. The application of this method to a flow in horizontal channel, taken as an experimental device, is presented. The results of computations are compared with experimental data...

The study of turbulence near walls has experienced a renaissance in the last decade, in part because of the availability of high-quality numerical simulations. The viscous and buffer layers over smooth walls are now fairly well understood. They are essentially independent of the outer flow, and there is a family of numerically-exact nonlinear structures that predict well many of the best-known characteristics of the wall layer, such as the intensity and the spectra of the velocity fluctuations,...

In the note we are concerned with higher regularity and uniqueness of solutions to the stationary problem arising from the large eddy simulation of turbulent flows. The system of equations contains a nonlocal nonlinear term, which prevents straightforward application of a difference quotients method. The existence of weak solutions was shown in A. Świerczewska: Large eddy simulation. Existence of stationary solutions to the dynamical model, ZAMM, Z. Angew. Math. Mech. 85 (2005), 593–604 and P....

Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}{\left(𝛺\right)}^3)$ are regular.