In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental contrast between downsampling high-resolution images and authentically emulating low-resolution physics. The former method conserves more of the underlying physics, surpassing the usual constraints of real-world scenarios. We propose a novel definition of super-resolution tailored for PDE-based problems. Instead of simply downsampling from a high-resolution dataset, we use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Employing a physics-infused UNet upscaling method, we demonstrate its efficacy across various 2D-CFD problems such as discontinuity detection in Burger's equation, Methane combustion, and fouling in Industrial heat exchangers. Our method enables the generation of fine-mesh solutions bypassing traditional simulation, ensuring considerable computational saving and fidelity to the original ground truth outcomes. Through diverse boundary conditions during training, we further establish the robustness of our method, paving the way for its broad applications in engineering and scientific CFD solvers.

翻译：在计算流体力学中，粗网格模拟虽具备计算效率，却常缺乏精度。将传统超分辨率技术应用于此类模拟面临重大挑战，原因在于对高分辨率图像进行下采样与真实模拟低分辨率物理过程之间存在根本性差异。前者保留了更多底层物理特性，超越了现实场景的常规约束。我们提出一种专为基于偏微分方程问题定制的超分辨率新定义：不采用从高分辨率数据集简单下采样的方法，而是以粗网格模拟数据作为输入，预测细网格模拟结果。通过采用物理信息融合的UNet升尺度方法，我们验证了该方法在多种二维计算流体力学问题（如Burger方程中的不连续性检测、甲烷燃烧、工业换热器结垢）中的有效性。该方法能绕过传统模拟直接生成细网格解，在显著节省计算资源的同时保持对原始真实结果的高保真度。通过在训练过程中引入多样化边界条件，我们进一步证实了该方法的鲁棒性，为其在工程与科学计算流体力学求解器中的广泛应用铺平了道路。