An efficient two-level factored method for advection-dispersion problem with spatio-temporal coefficients and source terms

Abstract

A two-level factored implicit scheme is considered for solving a two-dimensional unsteady advection-dispersion equation with spatio-temporal coefficients and source terms subjected to suitable initial and boundary conditions. The approach reduces multi-dimensional problems into pieces of one-dimensional subproblems and then solves tridiagonal systems of linear equations. The computational cost of the algorithm becomes cheaper and makes the method more attractive. Furthermore, the two-level approach is unconditionally stable, temporal second-order accurate and spatial fourth-order convergent. The developed numerical scheme is faster and more efficient than a broad range of methods widely studied in the literature for the considered initial-boundary value problem. The stability of the proposed procedure is analyzed in the $ L^{\infty}(t_{0}, T_{f}; L^{2}) $-norm whereas the convergence rate of the algorithm is numerically analyzed using the $ L^{2}(t_{0}, T_{f}; L^{2}) $-norm. Numerical examples are provided to verify the theoretical result.

Keywords

• two-dimensional advection-dispersion equation
• spatio-temporal coefficients
• crank-nicolson approach
• a two-level factored crank-nicolson method
• stability and convergence rate