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)

• Record Type: Journal Article
• Authors: Ngondiep, Eric
• Is Part Of: International journal for computational methods in engineering science and mechanics. Volume 22:Issue 4(2021)
• Page Start: 253
• Page End: 264
• Publication Date: 2021-07-04
• Subjects: Two-dimensional transport equation -- time dependent dispersion coefficients -- implicit method -- a fourth order two-level factored implicit scheme -- stability and convergence rate; 35K20 -- 65M06 -- 65M12; Engineering -- Data processing -- Periodicals; Engineering mathematics -- Periodicals; Computer-aided engineering -- Periodicals; 620.00420285
• DOI: 10.1080/15502287.2020.1856972
• Languages: English
• ISSNs: 1550-2287

Abstract

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.