Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme

Advances in Difference Equations

article

Bu, Sunyoung¹  Bak, Soyoon² 

[1] Department of Liberal Arts, Hongik University;Department of Mathematics, Kyungpook National University

关键词: Time-discretization method;    Semi-Lagrangian method;    Advection–diffusion equation;    Advection–dispersion equation;    Burgers’ equations;    Korteweg-de Vries–Burgers’ equation;   

DOI  :  10.1186/s13662-020-02580-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection–diffusion–dispersion problems. The third-order backward differentiation formula and fourth-order finite difference schemes are used in temporal and spatial discretizations, respectively. Additionally, to evaluate function values at non-grid points in BSL, the constrained interpolation profile method is used. Several numerical experiments demonstrate the efficiency of the proposed techniques in terms of accuracy and computation costs, compare with existing departure traceback schemes.

【 授权许可】

CC BY