发表机构
Università Politecnica delle Marche; CINECA（马尔凯理工大学; CINECA）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对大涡模拟中基于最小二乘的滤波宽度公式，分析浮点扰动的传播机制，提出压缩与调制方法以增强鲁棒性，并在异构CPU/GPU上验证其有效性。
AI 中文摘要
异构高性能计算架构使数值算法暴露于由浮点运算的非结合性引起的扰动中。在大涡模拟（LES）中，当这些数值效应影响进入亚格子尺度（SGS）模型的滤波宽度时，它们可能变得相关。本研究针对基于最小二乘（LSQ）的滤波宽度公式探讨了这一机制，重点关注浮点效应如何产生、传播以及与已解析流动耦合。我们表明，对于固定的已解析运动学，LSQ滤波宽度关于网格度量的扰动是对数非扩张的，但不是严格收缩的。因此，小扰动可能以很小的衰减通过强方向性的滤波宽度响应进行传播。为缓解这种敏感性，我们引入了一种基于解析速度梯度的有界调制以及方向性网格尺度的标量最大-最小压缩。所得公式通过滤波宽度算子重新路由浮点扰动，在保持原始LSQ构造的流动依赖特性的同时提高了鲁棒性。该框架在异构CPU和GPU架构上对Re=3900的圆柱绕流和Re=1600的泰勒-格林涡进行了评估。在前者中，当传播的扰动与剪切层转捩相互作用时，相对度量扰动的近乎一对一的传播可能变得相关。相比之下，在正交的泰勒-格林涡网格上，累积路径在结构上不存在，且没有出现可比较的宏观响应。这些结果表明，在异构计算环境中，浮点敏感性对LES滤波宽度公式很重要。
英文摘要
Heterogeneous high--performance computing architectures expose numerical algorithms to perturbations arising from the non--associativity of floating--point arithmetic. In Large--Eddy Simulation (LES), similar numerical effects may become relevant when they affect the filter--width entering the subgrid scale (SGS) model. This work investigates this mechanism for the least--squares (LSQ) based filter--width formulation, focusing on how floating--point effects are generated, transmitted, and coupled with the resolved flow. We show that, for fixed resolved kinematics, the LSQ filter--width is logarithmically non-expansive but not strictly contractive with respect to perturbations of the mesh metrics. Consequently, small disturbances may be transmitted with little attenuation through strongly directional filter-width responses. To mitigate this sensitivity, we introduce a scalar max--min compression of the directional mesh scales together with a bounded modulation based on the resolved velocity gradient. The resulting formulation reroutes floating--point perturbations through the filter-width operator, improving robustness while preserving the flow--dependent character of the original LSQ construction. The framework is assessed on heterogeneous CPU and GPU architectures for flow past a circular cylinder at Re=3900 and the Taylor--Green vortex at Re=1600. In the former, nearly one--to--one transmission of relative metric disturbances can become relevant when the transmitted perturbations interact with shear-layer transition. By contrast, on orthogonal Taylor--Green vortex grids, the accumulation pathway is structurally absent and no comparable macroscopic response develops. These results suggest floating--point sensitivity matters for LES filter--width formulations in heterogeneous computing environments.
