In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method...

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...

This paper is concerned with global solutions of the generalized Navier-Stokes equations. The generalized Navier-Stokes equations here refer to the equations obtained by replacing the Laplacian in the Navier-Stokes equations by the more general operator (−∆) with α > 0. It has previously been shown that any classical solution of the d-dimensional generalized NavierStokes equations with α ≥ 1 2 ...

We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as the skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes (RNS ) equations are defined on the boundary of the flow, and hence have reduced spatial dimensionality compared to the Navier-Stokes equations. This spatial reduction speeds up numer...

This paper is devoted to the study of a stationary problem consisting of the Boussinesq approximation of the Navier–Stokes equations and two convection–diffusion equations for the temperature and concentration, respectively. The equations are considered in 3D and a velocity–pressure formulation of the Navier–Stokes equations is used. The problem is complicated by nonstandard boundary conditions...

The incompressible Navier-Stokes equations are discretized in space and integrated in time by the method of lines and a semi-implicit method. In each time step a set of systems of linear equations has to be solved. The size of the time steps are restricted by stability and accuracy of the time-stepping scheme, and convergence of the iterative methods for the solution of the systems of equations...

In this paper, we present first-, second-, and third-order implicit finite-volume schemes for solving the Navier-Stokes equations on unstructured grids based on a hyperbolic formulation of the viscous terms. These schemes are first-, second-, and third-order accurate on irregular grids for both the inviscid and viscous terms and for all Reynolds numbers, not only in the primitive variables but ...