In this paper we present a seven-velocity three-dimensional (D3N7) vectorial lattice Boltzmann method (LBM) including various types of approximations to the pressure and propose a family of two-parameterized second-order boundary schemes with accuracy independent of the boundary location. In order to show the numerical stability of the D3N7 model, we construct a symmetrizer to handle the nonlinear approximations to the pressure. In the meantime, we relate the stability based on the vectorial model to that based on the conventional scalar model through an orthogonal similarity transformation. Finally, two 3-D examples with straight and curved boundaries numerically validate the D3N7 model, including linear and nonlinear approximations to the pressure, together with the proposed boundary schemes.

在本文中，我们提出了一种七速度三维（D3N7）矢量格子Boltzmann方法（LBM），其中包括各种类型的压力近似值，并提出了一系列精度与边界位置无关的两参数二阶边界方案。为了显示D3N7模型的数值稳定性，我们构造了一个对称器来处理压力的非线性近似。同时，通过正交相似度变换，将基于矢量模型的稳定性与基于常规标量模型的稳定性相关联。最后，两个具有直线和曲线边界的3-D实例在数值上验证了D3N7模型，包括对压力的线性和非线性近似，以及所提出的边界方案。