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首页> 外文期刊>Journal of Scientific Computing >Numerical Studies Based on Higher-Order Accuracy Lattice Boltzmann Model for the Complex Ginzburg-Landau Equation
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Numerical Studies Based on Higher-Order Accuracy Lattice Boltzmann Model for the Complex Ginzburg-Landau Equation

机译：基于高阶精度格子Boltzmann模型的复Ginzburg-Landau方程的数值研究

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摘要

In this paper, a higher-order accuracy lattice Boltzmann model for the complex Ginzburg-Landau equation is proposed. In order to obtain higher-order accuracy of truncation error and to overcome the drawbacks of "error rebound" in the previous models, a new assumption of additional distribution is presented to improve the accuracy of the model for the complex partial differential equation with nonlinear source term. As results, the complex Ginzburg-Landau equation is recovered with the fourth-order accuracy of truncation error. Based on this model, the problems of a single spiral wave in two-dimensional (2D) space and a single scroll in three-dimensional (3D) space are implemented to test the lattice Boltzmann scheme. The comparisons between the LBM results and the Alternative Direction Implicit results are given in detail. The numerical examples show that assumptions of source term can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the complex Ginzburg-Landau equation.
机译：针对复杂的Ginzburg-Landau方程，提出了一种高阶精度的格子Boltzmann模型。为了获得截断误差的高阶精度并克服先前模型中的“误差回弹”缺点，提出了附加分布的新假设，以提高带有非线性源的复杂偏微分方程模型的精度。术语。结果，复数的Ginzburg-Landau方程以截断误差的四阶精度被恢复。基于此模型，实现了二维（2D）空间中的单个螺旋波和三维（3D）空间中的单个涡旋的问题，以测试格子Boltzmann方案。详细介绍了LBM结果与“替代方向隐式”结果之间的比较。数值算例表明，对于复杂的Ginzburg-Landau方程，可以使用源项的假设来提高格Boltzmann格式的截断误差的准确性。

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