PARTICLE APPROXIMATION OF A LINEAR CONVECTION-DIFFUSION PROBLEM WITH NEUMANN BOUNDARY CONDITIONS

摘要

We present a particle method to solve numerically the linearized Navier-Stokes equation with Neumann boundary conditions on the vorticity. The method is based on the use of a boundary integral equation formulation and the introduction of cut-off functions. As a result of this formulation, the vorticity creation due to the boundary conditions is taken into account by the time evolution of the particle weights. The scheme is conservative in L(1) and positive in L(infinity) and L(2) if the cutoff is nonnegative. The stability of the method is proven with no condition on the viscosity, and the convergence of the approximate solution toward the solution of the advection-diffusion problem is established in L(infinity) and in L(2). [References: 28]