A fourth-order two-level factored implicit scheme for solving two-dimensional unsteady transport equation with time-dependent dispersion coefficients. Issue 4 (4th July 2021) - Ngondiep, Eric
Abstract: This paper analyzes a two-level factored implicit scheme in a numerical solution of two-dimensional unsteady advection-diffusion equation with time dependent dispersion coefficients subjects to initial and boundary conditions. The proposed approach is fast and efficient: unconditionally stable, second order accurate in time, spatial fourth order convergent and it requires less computing time. In fact, the two-level factored technique reduces to solve a tridiagonal system of linear equations at each calculation step. This reduces the computational cost of the algorithm. The analysis of the stability of the numerical scheme considers the L ∞ ( t 0, T f ; L 2 ) -norm while the error estimates and convergence rate use L 2 -norm. A wide set of numerical evidences are presented and discussed.