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（CFD）中，粗网格模拟虽能提升计算效率，但往往精度不足。将传统超分辨率应用于此类模拟面临重大挑战，因为高分辨率图像的下采样与真实低分辨率物理过程的模拟存在根本性差异：前者保留了更多内在物理信息，超出了现实场景的常规约束。我们针对基于偏微分方程的问题提出一种超分辨率的新定义：不采用高分辨率数据集的简单下采样，而是以粗网格模拟数据为输入，预测细网格模拟结果。通过采用物理信息融合的UNet上采样方法，我们在多种二维CFD问题（如Burger方程的不连续检测、甲烷燃烧及工业换热器结垢）中验证了其有效性。该方法可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保真度。通过训练过程中引入多样化的边界条件，我们进一步验证了该方法的鲁棒性，为其在工程与科学CFD求解器中的广泛应用奠定基础。