Various numerical boundary condition methods have been proposed to simulate various aspects of the no-slip wall condition using the Lattice Boltzmann Method. In this paper, a new boundary condition scheme is developed to model the no-slip wall condition in the presence of the body force term near the wall which is based on the Bennett extension. The error related to the new model is smaller tha...

Abstract We study the $$L^{\infty }$$ L ∞ stability of Navier-Stokes equations in half-plane with a viscosity-dependent Navier friction boundary condition around shear profiles which are linearly unstable for Euler equation. The dependence from viscosity is given as $$\...

Homotopy perturbation method HPM and boundary element method BEM for calculating the exact and numerical solutions of Poisson equation with appropriate boundary and initial conditions are presented. Exact solutions of electrostatic potential problems defined by Poisson equation are found using HPM given boundary and initial conditions. The same problems are also solved using the BEM. The cell i...

Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free bo...

Periodic travelling waves are a fundamental solution form in oscillatory reactiondiffusion equations. Here I discuss the generation of periodic travelling waves in a reaction-diffusion system of the generic λ-ω form. I present numerical results suggesting that when this system is solved on a semi-infinite domain subject to Dirichlet boundary conditions in which the variables are fixed at zero, ...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

2014 We derive a model of convection appropriate for containers with large width to height ratios. It couples a real rapidly varying convective variable to a slowly varying « drift » velocity field given by its stream-function. The derivation assumes stress-free boundary conditions at the top and the bottom. We discuss its extension to the more realistic no-slip case and the analogies/differenc...

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

where T ≥ 2 is a positive integer andΔu k u k 1 −u k is the forward difference operator. Throughout this paper, we denote by Z a, b the discrete interval {a, a 1, . . . , b}, where a and b are integers and a < b. We consider in 1.1 two different boundary conditions: a Dirichlet boundary condition u 0 0 and a Neumann boundary condition Δu T 0 . In the literature, the boundary condition considere...