Abstract A residual-based variational multi-scale (VMS) modeling framework is applied to simulate atmospheric flow over complex environmental terrains. The VMS framework is verified and validated using two test cases using linear finite element (FEM) and quadratic non-uniform rational B-spline (NURBS) discretizations. First, the flow over the 3D, axisymmetric Gaussian hill (normally distributed surface) is used to compare the results with FEM and NURBS discretization. Next, the actual terrain of the Bolund hill is used to demonstrate the efficacy of the framework. Good agreement with published data, coming from simulations and field measurements, is achieved, with the NURBS discretization showing much better per-degree-of-freedom accuracy compared with linear FEM. The paper includes a comprehensive review of experimental and numerical methods, and the corresponding challenges, for complex-terrain flows, which provides a proper context for the developments presented in this work.

中文翻译：

---

复杂环境地形上大气湍流的变分多尺度框架

摘要 应用基于残差的变分多尺度（VMS）建模框架来模拟复杂环境地形上的大气流动。使用线性有限元 (FEM) 和二次非均匀有理 B 样条 (NURBS) 离散化的两个测试案例验证和验证 VMS 框架。首先，使用 3D 轴对称高斯山丘（正态分布表面）上的流将结果与 FEM 和 NURBS 离散化进行比较。接下来，以博隆山的实际地形来演示框架的功效。与来自模拟和现场测量的已发布数据非常吻合，与线性 FEM 相比，NURBS 离散化显示出更好的每自由度精度。该论文包括对实验和数值方法的全面回顾，