DIFFERENTIAL DISTANCE FUNCTION COMPUTATIONS FOR MESH GENERATION

从本质上讲，距离函数（原始和修改的最近表面距离）需要用于RANS （Reynolds平均纳维-斯托克斯）湍流建模，多相和自由表面流动的一般计算界面跟踪，静电库仑力建模以及火焰前和爆炸建模以及光学和声学的光线跟踪。它们还可用于捕获微尺度流动中的克努森层效应，并用于实施海绵和各种其他数值波反射阻尼策略和LES（大涡模拟）的稳定措施。此外，它们还可用于实现混合les - ran策略。距离函数，在某些情况下可以使用昂贵的搜索操作来评估。或者，微分方程也可以求解。在这里，建议探索非结构化（其中各种细胞形状可以以灵活的方式进行细分）移动和覆盖网格上的微分距离函数方程的解，以产生上述通用CFD代码非常需要的功能。使用这种网格的流量解决方案越来越普遍。然而，鲁棒网格生成仍然是一个重大的挑战。如果使用六面体单元和它们提供的更高的数值保真度，则尤其如此。因此，本文还建议探索使用新的基于微分距离函数相关方程的方法：混合网格生成（六面体边界层单元连接到边界层外的四面体单元）；纯六面体网格生成和覆盖网格计算接口定位。所探讨的微分方程将包括双曲型Eikonal、Hamilton-Jacobi和椭圆型泊松。将特别注意使用有限元、有限体积和边界元方法在混合单元拓扑的运动、非结构化过集网格上经济而准确地求解这些方程。

Essentially, distance functions (raw and modified nearest surface distances) are needed for RANS (Reynolds Averaged Navier-Stokes) turbulence modelling, general computational interface tracking for multiphase and free surface flows, electrostatic Coulomb force modelling and also flame front and explosion modelling along with ray tracing for optics and acoustics. They can also be used to capture Knudsen layer effects in microscale flows and for the implementation sponges and various other numerical wave reflection damping strategies and stabilising measures for LES (Large Eddy Simulation). Furthermore they can be used to implement hybrid LES-RANS strategies. Distance functions, can under certain circumstances be evaluated using expensive search operations. Alternatively, differential equations can be solved. Here, it is proposed to explore the solution of differential distance function equations on unstructured (where a wide range of cell shapes can be tessellated in a flexible fashion) moving and overset meshes to yield the above noted capabilities which are highly desirable for general purpose CFD codes. Flow solutions using such grids are increasingly common. However, robust mesh generation still presents a significant challenge. This is especially so if use is made of hexahedral cells and the higher numerical fidelity that they provide. Hence, here it is proposed to also explore the use of novel differential distance function related equation based approaches for: hybrid grid generation (hexahedral boundary layer cells linked to tetrahedral cells outside the boundary layer); pure hexahedral grid generation and overset grid computational interface location. The differential equations explored will include the hyperbolic Eikonal, Hamilton-Jacobi and elliptic Poisson. Especial attention will be paid to the economical and accurate solution of these equations on moving, unstructured over-set grids with mixed element topologies using finite element, finite volume & boundary element methods.