论文标题
构建晶格玻尔兹曼方法的松弛系统
Constructing relaxation systems for lattice Boltzmann methods
论文作者
论文摘要
我们介绍了第一个用于构建d维的晶格玻尔兹曼方法（LBM）的自上而下的ANSATZ。特别是，我们为给定标量，线性，D维对流扩散方程构建了一个松弛系统（RS）。随后，RS与零件和第一个能量壳上的D维离散速度Boltzmann模型（DVBM）相关。进行平衡，力矩空间和碰撞算子的代数表征。此外，RS的封闭方程式表达了添加的弛豫项，因为预保守数量的预先成分的高阶衍生物。在这里，将广义（2D+1）x（2d+1）rs链接到DDQ（2D+1）DVBM，该DVBM在完全离散后产生了一个LBM，其空间和时间上具有二阶精度。证明了最终LBM的DVBM的任意比例，DVBM的任意缩放结果的严格合并结果。自上而下的构造LBM在多个GPU上进行了数值测试，其中几个网格归一化的非二维数字在d = 3尺寸中具有光滑且非平滑的初始数据。
We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) for a given scalar, linear, d-dimensional advection-diffusion equation. Subsequently, the RS is linked to a d-dimensional discrete velocity Boltzmann model (DVBM) on the zeroth and first energy shell. Algebraic characterizations of the equilibrium, the moment space, and the collision operator are carried out. Further, a closed equation form of the RS expresses the added relaxation terms as prefactored higher order derivatives of the conserved quantity. Here, a generalized (2d+1)x(2d+1) RS is linked to a DdQ(2d+1) DVBM which, upon complete discretization, yields an LBM with second order accuracy in space and time. A rigorous convergence result for arbitrary scaling of the RS, the DVBM and conclusively also for the final LBM is proven. The top-down constructed LBM is numerically tested on multiple GPUs with smooth and non-smooth initial data in d=3 dimensions for several grid-normalized non-dimensional numbers.
