论文标题
过滤的晶格玻尔兹曼碰撞配方执行各向同性和伽利亚不变性
Filtered Lattice Boltzmann Collision Formulation Enforcing Isotropy and Galilean Invariance
论文作者
论文摘要
过滤的晶格玻尔兹曼碰撞操作员公式的中心框架是去除给定晶格速度集的各向同性阶层所支持的流体动力矩。由于Hermite多项式的自然力矩正交性，因此通过Hermite膨胀直接获得过滤后的碰撞算子的形式。在本文中，我们提出了过滤后的碰撞操作员公式的扩展，以实现伽利亚的不变性。这是通过在相对参考框架中相对于局部流体速度表示的流体动力矩来完成的。由此产生的碰撞算子具有紧凑且完全伽利亚的形式，然后可以通过无限的Hermite膨胀来精确表达。可以直接确定给出各向同性的特定顺序的晶格速度集。如果使用高阶晶格速度集，则将高阶项保留在截断中，以便渐近地达到伽利亚的不变性。先前已知的过滤碰撞算子形式可以看作是零流体速度的极限。
The central framework of a filtered lattice Boltzmann collision operator formulation is to remove hydrodynamic moments that are not supported by the order of isotropy of a given lattice velocity set. Due to the natural moment orthogonality of the Hermite polynomials, the form of a filtered collision operator is obtained directly via truncation of the Hermite expansion. In this paper, we present an extension of the filtered collision operator formulation to enforce Galilean invariance. This is accomplished by representing hydrodynamic moments in the relative reference frame with respect to local fluid velocity. The resulting collision operator has a compact and fully Galilean invariant form, and it can then be exactly expressed in terms of an infinite Hermite expansion. Giving a lattice velocity set of specific order of isotropy, a proper truncation of this expansion can be directly determined. Higher order terms are retained in the truncation if a higher order lattice velocity set is used, so that Galilean invariance is attained asymptotically. The previously known filtered collision operator forms can be seen as a limit of zero fluid velocity.
