Industrialization of High-Order Unstructured Methods for Computational Fluid Dynamics

加拿大承诺到2030年将温室气体排放量减少40-45%，到2050年实现净零排放。这些目标将依赖于改善运输系统、发电、替代燃料、氢燃烧和工业流程。改进这些系统越来越依赖于我们使用计算流体动力学（CFD）进行准确性能预测的能力。绝大多数CFD从业者依赖于reynolds -average Navier-Stokes （RANS）方法进行设计，仅解决时间平均流动问题，并依赖于近似湍流模型。然而，众所周知，RANS湍流模型的局限性限制了它们在工程设计空间中相对较小的区域的使用，因为它们无法准确预测分离或过渡的湍流。为了解决这些问题，包括大涡模拟（LES）在内的新一代非定常尺度解析CFD技术已被提出作为下一代设计的支持技术。使用LES大大提高了精度，但也大大增加了计算成本。为了解决这个问题，新一代的高阶非结构化CFD方法，包括不连续Galerkin和通量重建方法，已经被开发出来。这些方案可以利用现代硬件架构（如图形处理单元）的计算能力，以更低的计算成本提供数量级更精确的结果。然而，它们的工业采用受到三个主要因素的限制：有效的时间步进技术的可用性，可证明的非线性稳定方案的制定，以及定制的非线性求解器技术。因此，这三个因素是目前活跃的研究领域，每个都是该计划申请人的直接关注点。重要的是，这些因素都是高度耦合的，预计通过团队解决这些问题，我们将能够在工业CFD中使用的数值方法中产生一步变化。最终，这将使LES在工业规模上的应用成为可能，提高工程性能预测的准确性，并有助于实现加拿大的减排目标。

Canada has committed to reducing greenhouse gas emissions by 40-45% by 2030, and reaching net-zero by 2050. These goals will rely on improving transportation systems, power generation, alternative fuels, Hydrogen combustion, and industrial processes. Improving these systems relies, increasingly, on our ability to make accurate performance predictions using Computational Fluid Dynamics (CFD).The vast majority of CFD practitioners rely on the Reynolds-Averaged Navier-Stokes (RANS) approach for design, resolving only the time-average flow and relying on approximate turbulence modelling. However, the well-known limitations of RANS turbulence models restricts their use to a relatively small region of the engineering design space, as they are unable to accurately predict separated or transitional turbulent flows. To address these limitations, a new generation of unsteady scale-resolving CFD techniques, including Large-Eddy Simulation (LES), have been proposed as enabling technologies for next-generation design.Using LES significantly improves accuracy, but also greatly increases computational cost. To address this, a new generation of high-order unstructured CFD methods, including the Discontinuous Galerkin and Flux Reconstruction approaches, have been developed. These schemes can leverage the compute capability of modern hardware architectures, such as Graphical Processing Units, to provide orders of magnitude more accurate results at reduced computational cost. Nevertheless, their industrial adoption is limited by three primary factors: the availability of efficient time-stepping techniques, the formulation of provably non-linearly stable schemes, and bespoke non-linear solver technologies. It follows that these three factors are currently active areas of research, with each being the direct focus of one applicant to this program. Importantly, these factors are all highly coupled and it is expected that, by addressing these as a team, we will be able to seed a step change in the numerical methods used for industrial CFD. Ultimately, this will enable the use of LES at industrial scale, improve the accuracy of engineering performance predictions, and contribute to meeting Canada's emissions reduction targets.