Search results for "Navier-Stokes"

A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations

1992

The tradìtíonal splitting-up method or fractíonal step method is stuítable for sequentìal compulìng. Thís means that the computing of the present fractional step needs the value of the previous fractional steps. In thìs paper we propose a new splitting-up scheme for which the computing of the fractional steps is índependent of each other and therefore can be computed by parallel processors. We have proved the convergence estimates of this scheme both for steady state and nonsteady state linear and nonlinear problems. To use .finite element method to solve Navier-Stokes problems it is always dfficult to handle the zero-divergent finíte element spaces. Here, by using the splitting-up method w…

Nonlocal boundary conditions for the Navier-Stokes equations

2006

Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag

2014

We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

2006

Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment [ A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000) ; A. Gailitis et al., Physics of Plasmas 11, 2838 (2004) ], consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeled by a finite-volume Navi…

Drops moving in flow with chernical reaction

1994

We propose a free boundary model described by coupled Navier-Stokes and chemical reaction equations with discontinuous coefRcients to simulate the chemical re- ¿ctions in viscous drops moving in a viscous incompressible ûuid. Approximation of the solution by a special ñnite element method (FEM) with a method of mapping is discussed. Several numerical resulùs åre presented.

Complex singularity analysis for vortex layer flows

2021

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstro…

The inviscid limit and Prandtl's asymptotic expansion for incompressible flows in the half space

2022

The validity of the inviscid limit for the incompressible Navier-Stokes equations is one of the most important and challenging problems in the mathematical theory of fluid dynamics: the motion of inviscid fluids is described by the Euler equations, so, when the viscosity goes to zero, one would expect the convergence of NS solutions to the Euler solutions. However, NS equations are a singular perturbation of the Euler equations: the change of order of the equation implies that fewer boundary conditions can be imposed on the inviscid flows. Therefore, the no-slip boundary conditions, imposed on the NS solutions, are not satisfied by the Euler flow, for which a tangential slip is allowed. Thi…

The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow

2008

We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…

Filtering of the Navier-Stokes Equations in the Context of Time-Dependent Flows

1998

Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions

2010

In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…