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Chen, C., Zhang, X. and Liu, Z. (2020) A High-Order Compact Finite Difference Scheme and Precise Integration Method Based on Modified Hopf-Cole Transformation for Numerical Simulation of N-Dimensional Burgers’ System. Applied Mathematics and Computation, 372, Article ID: 125009.
https://doi.org/10.1016/j.amc.2019.125009

has been cited by the following article:

• TITLE: Discrete Transparent Boundary Conditions for Burgers’ Equation

  AUTHORS: Xinyue Chen, Wenqing Zhang, Yuchen Wu

  KEYWORDS: Burgers’ Equation, Cole-Hopf Transformation, Discrete Transparent Boundary Conditions

  JOURNAL NAME: Engineering, Vol.16 No.12, December 30, 2024

  ABSTRACT: This paper is devoted to numerically solving the Burgers’ equation in unbounded region, which describes the nonlinear wave propagation and diffusion effect. How to numerically and efficiently solve this problem remains a challenge due to the principal difficulties of not only the unboundedness but also nonlinearity. This paper aims to design the discrete transparent boundary conditions of Burgers’ equation to overcome the unboundedness. The presence of a nonlinear term in the equation makes it challenging to derive suitable artificial boundary conditions. To deal with the nonlinear term, a linear parabolic equation is obtained by applying the well-known Cole-Hopf transformation to the Burgers’ equation. Employing the Z -transformation, we then establish the discrete transparent boundary conditions for the linearized problem. Subsequently, the original equation is reduced to an initial boundary value problem, that can be efficiently solved by the finite difference method. The numerical analysis is reported rigorously. Some numerical results are given to demonstrate the accuracy and feasibility of the proposed method.