Abstract We consider the virtual element discretization of Navier–Stokes equations coupled with heat equation where viscosity depends on temperature. present problem, show its well-posedness and prove optimal error estimates. Numerical experiments that confirm theoretical bounds are also presented.

Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...

We show several basic properties concerning the relation between the Stokes geometry (i.e., configuration of Stokes curves and turning points) of a higher order Painlevé equation with a large parameter and the Stokes geometry of (one of) the underlying Lax pair. The higherorder Painlevé equation with a large parameter to be considered in this paper is one of the members of PJ -hierarchy with J ...

This paper presents an incompressible smoothed particle hydrodynamics (SPH) model to simulate wave propagation in a free surface flow. The Navier-Stokes equations are solved in a Lagrangian framework using a three-step fractional method. In the first step, a temporary velocity field is provided according to the relevant body forces. This velocity field is renewed in the second step to include t...

Sediment flushing of reservoirs is an operational technique, whereby previously accumulated sediments in the reservoirs are hydraulically removed by accelerated flow when the bottom desiltingoutlets of the dam are opened. In this research, the process of sediment flushing is simulated by a three dimensional numerical model in which sediment and flow interaction are reflected in the reservoirs. ...

We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equa...

Abstract. A simple algorithm of iterative substructuring method as the same way of elasticity problem is proposed for a discretized Stokes equation by P1/P1 element and penalty stabilization technique. Owing to the stability term, solvabilities of local Dirichlet problem, of local Neumann problem for preconditioner, and of the coarse space problem are ensured. Conjugate gradient method with pre...

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...

a novel computational fluid dynamics and molecular kinetic theory (cfd-mk) method was developed to simulate the impingement of a nanodroplet onto a solid surface. a numerical solution of the navier–stokes equation using a volume-of-fluid (vof) technique was used to model nanodroplet deformation. dynamic contact angle during droplet impact was obtained by molecular kinetic theory. this dynamic c...