A fourth-order block-centered compact difference scheme for nonlinear contaminant transport equations with adsorption

• Published in: Applied numerical mathematics 2022-01, Vol.171, p.212-232
• Main Authors: Shi, Yilei, Xie, Shusen, Liang, Dong
• Format: Article
• Language: English
• Subjects: Block-centered mesh; Compact difference; Error estimate; Mass conservation; Nonlinear contaminant transport; Stability
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2021.09.003

•It is important to develop numerical schemes for nonlinear contaminant transports in porous media.•We develop a new fourth-order block-centered compact difference scheme of solution and flux for nonlinear transports with adsorption.•The developed scheme is proved to be mass conservative and unconditionally stable.•The developed scheme is proved to have fourth-order error estimate under smooth regularity of solution.•Numerical experiments show excellent performance of the proposed scheme. Nonlinear contaminant transports through porous media are important in many scientific and engineering applications. In this paper, we develop and analyze fourth-order block-centered compact difference scheme (BCCDS) for the nonlinear contaminant transport equations with adsorption process in porous media. Based on block-centered mesh, a fourth order compact difference scheme of solution and its flux is derived. We prove the mass conservation of the proposed scheme and its unconditional stability. We analyze the convergence and obtain the fourth-order error estimate under the smooth regularity of exact solution. Numerical experiments are presented to show the performance of the schemes.