论文标题
限制晶格玻尔兹曼方程的一致性
Limit Consistency of Lattice Boltzmann Equations
论文作者
论文摘要
我们将极限一致性的概念作为模块化部分，以证明与给定的部分微分方程（PDE）系统相对于晶格Boltzmann方程（LBE）的一致性。不可压缩的Navier-Stokes方程（NSE）用作典范。基于Bhatnagar-Gross-Krook（BGK）Boltzmann方程向NSE的流体动力极限，我们通过嵌套常规的Taylor扩展和有限差异来提供连续的离散化。我们跟踪粒子分布函数域的离散状态，并在派生过程中所有级别的截断误差。通过参数化方程并证明各个方程家族的极限一致性，我们在离散化的每个步骤中保留了靶向PDE的路径，即，对于离散的速度BGK Boltzmann方程和时空离散的LBE。作为一个直接的结果，我们将晶格Boltzmann方法的离散化技术展现为有限的差异，并提供了数值方案的通用自上而下的推导，以维持连续限制。
We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equation (PDE) system. The incompressible Navier--Stokes equations (NSE) are used as paragon. Based upon the hydrodynamic limit of the Bhatnagar--Gross--Krook (BGK) Boltzmann equation towards the NSE, we provide a successive discretization by nesting conventional Taylor expansions and finite differences. We track the discretization state of the domain for the particle distribution functions and measure truncation errors at all levels within the derivation procedure. Via parametrizing equations and proving the limit consistency of the respective families of equations, we retain the path towards the targeted PDE at each step of discretization, i.e. for the discrete velocity BGK Boltzmann equations and the space-time discretized LBEs. As a direct result, we unfold the discretization technique of lattice Boltzmann methods as chaining finite differences and provide a generic top-down derivation of the numerical scheme which upholds the continuous limit.
