In this paper, a family of stencil selection algorithms is presented for WENO schemes on unstructured meshes. The associated freedom of stencil selection for unstructured meshes, in the context of WENO schemes present a plethora of various stencil selection algorithms. The particular focus of this paper is to assess the performance of various stencil selection algorithm, investigate the parameters that dictate their robustness, accuracy and computational efficiency. Ultimately, efficient and robust stencils are pursued that can provide significant savings in computational performance, while retaining the non-oscillatory character of WENO schemes. This is achieved when making the stencil selection algorithms adaptive, based on the quality of the cells for unstructured meshes, that can in turn reduce the computational cost of WENO schemes. For assessing the performance of the developed algorithms well established test problems are employed. These include the least square approximation of polynomial functions, linear advection equation of smooth functions and solid body rotation test problem. Euler and Navier-Stokes equations test problems are also pursued such as the Shu-Osher test problem, the Double Mach Reflection, the supersonic Forward Facing step, the Kelvin-Helmholtz instability, the Taylor-Green Vortex, and the flow past a transonic circular cylinder.

本文针对非结构化网格上的WENO方案，提出了一系列的模板选择算法。在WENO方案的上下文中，非结构化网格的模板选择的相关自由度提供了多种模板选择算法。本文的重点是评估各种模板选择算法的性能，研究决定其鲁棒性，准确性和计算效率的参数。最终，人们追求的是高效而坚固的模板，可以在节省计算性能的同时保留WENO方案的非振荡特性。当基于非结构化网格的单元质量使模板选择算法自适应时，可以实现此目的，从而可以减少WENO方案的计算成本。为了评估已开发算法的性能，采用了公认的测试问题。这些包括多项式函数的最小二乘逼近，光滑函数的线性对流方程和固体旋转测试问题。还寻求Euler和Navier-Stokes方程测试问题，例如Shu-Osher测试问题，Double Mach反射，超音速正向步阶，Kelvin-Helmholtz不稳定性，Taylor-Green涡旋以及通过跨音速圆的流动柱面。