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.

中文翻译：

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基于复合时间离散方案的对流-扩散-弥散方程的仿真

摘要

在这项工作中，我们在后向半拉格朗日框架（BSL）中开发了一种基于经典搭配和积分递延校正方法的高阶复合时间离散方案，以模拟非线性对流-扩散-色散问题。在时间和空间离散化中分别使用三阶后向微分公式和四阶有限差分方案。另外，要评估BSL中非网格点处的函数值，使用了受约束的插值轮廓法。与现有的出发回溯方案相比，一些数值实验证明了所提技术在准确性和计算成本方面的效率。