We present in this paper a rigorous error analysis of certain projection schemes for the approximation of the unsteady incompressible Navier-Stokes equations. The error analysis is accomplished by interpreting the respective projection schemes as second-order time discretizations of a perturbed system which approximates the Navier-Stokes equations. Numerical results in agreement with the error ...

Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Ch...

In this work we present a technique of fast numerical computation for solutions of Navier-Stokes equations in the case of flows of industrial interest. At first the partial differential equations are translated into a set of nonlinear ordinary differential equations using the geometrical shape of the domain where the flow is developing, then these ODEs are numerically resolved using a set of co...

this paper presents the results of numerical simulations of the laminar and turbulent flows inside diverging channels using random vortex methods (rvm). random vortex method is a mesh-free method which solves unsteady vorticity equation instead of solving navier-stokes equations directly to determine the velocity field. in this paper, the velocity potential, which is used as the initial conditi...

A stochastic model corresponding to a simplified Hookean dumbbells viscoelastic fluid is considered, the convective terms being disregarded. Existence on a fixed time interval is proved provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem.

We study convection of an incompressible Newtonian fluid heated from below in a two-dimensional domain of height H: the Bénard problem. The lower wall is maintained at a temperature θbottom and the upper wall is maintained at a temperature θtop, where θbottom > θtop . The governing equations are the (2D) Navier–Stokes equations under the Boussinesq approximation, in which all variations in phys...

We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang –Mills theory and discuss its meaning. Then we move to ‘gravitational Wilson loops’, i.e. to holonomies in curved d = 2, 3, 4 spaces and derive ‘non-Abelian Stokes theorems’ for these quantities as well, which are similar to our formula in the Yang–Mills theory. In particular we derive an elegant formula for the holonomy i...

We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the stro...