关于压缩可动Navier-Stokes方程的相对速度格子Boltzmann方案稳定性研究
On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations
AI总结：
本文研究了用于可压缩Navier-Stokes方程的二维相对速度方案的稳定性特性，通过线性与非线性测试案例分析，揭示了动量选择对稳定性的影响。
摘要：
本文研究了用于可压缩Navier-Stokes方程的二维相对速度方案的稳定性特性。该方案受级联方案启发，具有在空间和时间函数中以速度场为参数的松弛特性。首先在线性背景下研究其稳定性，然后在Kelvin-Helmholtz不稳定性非线性测试案例中进行验证。揭示了动量选择对稳定性的影响。级联方案的动量集提高了d'Humières方案在小粘性情况下的稳定性。相反，常规动量集的相对速度方案会降低稳定性。
英文摘要：
This paper studies the stability properties of a two dimensional relative velocity scheme for the Navier-Stokes equations. This scheme inspired by the cascaded scheme has the particularity to relax in a frame moving with a velocity field function of space and time. Its stability is studied first in a linear context then on the non linear test case of the Kelvin-Helmholtz instability. The link with the choice of the moments is put in evidence. The set of moments of the cascaded scheme improves the stability of the d'Humières scheme for small viscosities. On the contrary, a relative velocity scheme with the usual set of moments deteriorates the stability.
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