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Parametric schemes for the simulation of the advection process in finite-difference-based single-relaxation-time lattice Boltzmann methods
Journal of Computational Science ( IF 3.3 ) Pub Date : 2020-06-12 , DOI: 10.1016/j.jocs.2020.101151
Gerasim V. Krivovichev

The paper is devoted to the analysis of two parametric explicit finite-difference schemes for the linear advection equations, considered on the advection step of the splitting algorithm of the finite-difference-based single-relaxation-time lattice Boltzmann method. The schemes are constructed by the approximation of the terms with the spatial derivatives at the characteristic directions. It is demonstrated that by the proper choice of the parameter values, the third and fourth accuracy orders are realized.

The stability analysis is based on the von Neumann method. As a result, the stability conditions as the inequalities on the values of the Courant–Friedrichs–Lewi number are obtained. It is demonstrated that the proposed schemes have better stability properties than the other high-order schemes and schemes with the spatial approximations at the Cartesian axes directions. It is demonstrated that the spurious numerical effects can be diminished by the proper choice of the parameter values.

The obtained theoretical results are confirmed by the solution of numerical examples with the smooth and discontinuous initial conditions.



中文翻译:

基于有限差分的单松弛时间晶格玻尔兹曼方法中对流过程模拟的参数方案

本文针对线性对流方程的两个参数显式有限差分方案进行了分析,并考虑了基于有限差分的单松弛时间格子Boltzmann方法的分解算法的对流步骤。通过在特征方向上用空间导数对项进行近似来构造这些方案。已经证明,由参数值的正确选择,在第三和第四准确性订单实现。

稳定性分析基于von Neumann方法。结果,获得了稳定性条件,即库兰特-弗里德里希斯-刘易斯数的值的不等式。结果表明,所提出的方案具有比其他高阶方案和在笛卡尔轴方向上具有空间近似的方案更好的稳定性。据表明,杂散数值效果可以通过参数值的适当选择而减少。

通过对具有光滑和不连续初始条件的数值示例进行求解,证实了所获得的理论结果。

更新日期:2020-06-12
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