The solution of the nonlinear Poisson-Boltzmann equation using lattice-Boltzmann

Abstract

In this paper we present the solution of the Poisson-Boltzmann equation using the Lattice-Boltzmann method. In order to obtain the solution, we use a redefinition of tensor n°, which is declared as a symmetric tensor whose diagonal components are chosen as the second derivative in time of the first moment of the distribution function, and the components outside of the diagonal give account of the nonlinear terms. The results are presented in two dimensions employing the D2Q9 lattice velocity scheme. We obtain results for the scalar field and its gradient for several kinds of initial conditions.