A fourth-order two-level factored implicit scheme for solving two-dimensional unsteady transport equation with time-dependent dispersion coefficients

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 $L^{\infty }(t_0,T_f;L^2)$-norm while the error estimates and convergence rate use L²-norm. A wide set of numerical evidences are presented and discussed.

Keywords:

• Two-dimensional transport equation
• time dependent dispersion coefficients
• implicit method
• a fourth order two-level factored implicit scheme
• stability and convergence rate

AMS SUBJECT CLASSIFICATION (MSC):

• 35K20
• 65M06
• 65M12

Acknowledgment

The author thanks the anonymous referee for interesting remarks which helped to improve the quality of the literature provided in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the Deanship of Scientific Research of Al-Imam Muhammad Ibn Saud Islamic University (IMSIU) under the Grant No. 331203.