Hybrid Hamilton-Jacobi-Poisson wall distance function model
Hybrid Hamilton-Jacobi-Poisson wall distance function model
复制标题
混合 Hamilton-Jacobi-Poisson 壁距离函数模型
DOI：
10.1016/j.compfluid.2010.12.021
复制
发表时间：
2011
影响因子：
2.8
通讯作者：
Tucker P
中科院分区：
文献类型：
--
作者：
Tucker P
计算壁面距离的成本很高，用于关键湍流模型和外围物理模型。本文提出了一种基于微分方程的距离估计算法，该算法具有潜在的经济性、鲁棒性、易于并行处理、精度提高等优点。它是混合的，部分利用近似泊松方程。这也允许估计辅助的前传播方向/速度信息，有效地给出壁法线。在程函方程（壁距的精确微分方程）的近似解中，可以充分利用泊松法向。可替代地，可以使用该泊松前沿方向（有效地，前沿速度，就程函方程输入而言）信息的加权分数和程函方程所暗示的加权分数。这两种方法都是一种混合Poisson-Eikonal壁距算法。为了提高壁距函数与湍流物理的兼容性，在程函方程中加入了拉普拉斯算子。这给出了所谓的哈密顿-雅可比方程。这种混合Poisson-Hamilton-Jacobi方法被认为是强大的质量差的网格。鲁棒性主要是由于泊松方程的椭圆背景存在。该椭圆分量通过双曲程函方程元素防止从固体表面传播的波前反射离开快速变化的网格密度的区域。在这种反射（由于网格质量差）是极端的情况下，波前速度信息从泊松方程到汉密尔顿-雅可比方程的转换可以更渐进地完成。与湍流建模物理学一致，在用户控制下，混合方程可以在凸表面周围强烈高估距离函数，而在凹表面周围低估距离函数。如果前一种特性不受欢迎，那么目前的方法可以适用于区域化。这样，泊松元素会自动移除凸几何区域周围的元素。
Expensive to compute wall distances are used in key turbulence models and also for the modeling of peripheral physics. A potentially economical, robust, readily parallel processed, accuracy improving, differential equation based distance algorithm is described. It is hybrid, partly utilising an approximate Poisson equation. This also allows auxiliary front propagation direction/velocity information to be estimated, effectively giving wall normals. The Poisson normal can be used fully, in an approximate solution of the eikonal equation (the exact differential equation for wall distance). Alternatively, a weighted fraction of this Poisson front direction (effectively, front velocity, in terms of the eikonal equation input) information and that implied by the eikonal equation can be used. Either results in a hybrid Poisson–eikonal wall distance algorithm. To improve compatibility of wall distance functions with turbulence physics a Laplacian is added to the eikonal equation. This gives what is termed a Hamilton–Jacobi equation. This hybrid Poisson–Hamilton–Jacobi approach is found to be robust on poor quality grids. The robustness largely results from the elliptic background presence of the Poisson equation. This elliptic component prevents fronts propagated from solid surfaces, by the hyperbolic eikonal equation element, reflecting off zones of rapidly changing grid density. Where this reflection (due to poor grid quality) is extreme, the transition of front velocity information from the Poisson to Hamilton–Jacobi equation can be done more gradually. Consistent with turbulence modeling physics, under user control, the hybrid equation can overestimate the distance function strongly around convex surfaces and underestimate it around concave. If the former trait is not desired the current approach is amenable to zonalisation. With this, the Poisson element is automatically removed around convex geometry zones.