论文标题
晶格Boltzmann方案的结构稳定性
Structural stability of Lattice Boltzmann schemes
论文作者
论文摘要
这项工作的目的是通过双曲线ANSATZ来确定晶格玻尔兹曼方案的行进孤立波解决方案类别。结果表明，在非线性波方程的有限差异溶液中可能发生虚假的孤立波。这种伪造的孤立波的发生表现出很长的寿命，导致在无界数值域中任意时间内的任意时间造成了不变的数值误差。此处将这种行为称为该方案的结构不稳定性，因为数值方案所跨越的解决方案的空间包含不是原始连续方程的解决方案的解决方案的类型（孤立波）。本文将有关古典方案的先前工作扩展到了晶格Boltzmann计划。
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to Lattice Boltzmann schemes.
