Abstract
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.
Highlights
1 Introduction This study focuses on the advection–diffusion–dispersion equation described as
Many physical phenomena can be described by the advection–diffusion or advection– dispersion equations, including various nonlinear time-dependent partial differential equations (PDEs), such as the Burgers-type and Korteweg–de Vries (KdV) type equations
We propose an adaptable high-order backward semi-Lagrangian method (BSL) with good stability to solve nonlinear advection–diffusion–dispersion equations
Summary
Where u := u or [u, v]T denotes the solution of (1); ν is a positive kinematic viscosity; μ is a dispersive coefficient; J := ux or ux vx uy vy. In the conventional BSL, several approximate methods are required to solve (3) simultaneously with (2): time and spatial discretization methods for (3), a departure traceback method for nonlinear ordinary differential equation (2), and an interpolation scheme to obtain the solution at non-Eulerian grid points. These approximate methods affect the overall time-to-space accuracy of the BSL.
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