Improving Finite Volume Methods for Industrial CFD: Adaptation, Error Quantification, and Robust Convergence

随着计算机能力的增长，使用计算流体动力学（CFD）模拟的问题的复杂性也在迅速增长。同时也更加强调对模拟结果的准确性进行量化。用于此任务的现有技术通常需要大量的计算资源。为了满足这一需求，需要一种新的范式，在这种范式中，具有自适应和误差量化能力的鲁棒流求解器可靠地产生具有已知误差范围的解决方案，而人工干预最少。该项目将为估算和减少模拟流动问题中的数值误差的新技术提供原型，并使商业CFD软件更高效，能够更可靠地计算解决方案。我们将在与现代商业CFD求解器中采用的二阶非结构化网格有限体积方法兼容的统一框架中进行这项工作。我们预计，这些进步可以在两到五年内开始应用于当前的商业CFD解决方案。我们还将与ANSYS Canada合作，评估在我们之前的合作项目中开发的新算法的使用情况，并结合他们现有的商业流量求解器。虽然目前的工作将集中在二阶方法上，但我们预计更精确的有限体积方法将迁移到商业CFD求解器中，我们将计划一个明确的升级路径，在5到10年的时间框架内为高阶方法提供适应性和鲁棒性改进。这些进步将为我们在该项目的工业合作伙伴ANSYS Canada提供重要的竞争优势，因为该供应商的软件将率先提供这些功能。反过来，他们的加拿大客户将通过使用CFD提高模拟结果的准确性和信心以及提高工程师的生产力而受益。

As computer power has grown, the complexity of problems simulated using computational fluid dynamics (CFD) has grown apace. Greater emphasis is also being placed on quantifying the accuracy of simulation results. Existing techniques for this task often have prohibitively large computational resource requirements.Addressing this need requires a new paradigm in which a robust flow solver with adaptive and error quantification capabilities reliably produces solutions with known error bounds with minimal human intervention. This project will prototype new techniques for estimating and reducing numerical error in simulation of flow problems, and for making commercial CFD software more efficient and able to compute solutions more robustly. We will do this work in a unified framework compatible with the second-order unstructured mesh finite volume methods employed in modern commercial CFD solvers. We expect that these advances can begin to be deployed in current commercial CFD solvers within two to five years. We will also work with ANSYS Canada to assess the use of new algorithms developed in our previous collaborative project in combination with their existing commercial flow solver. While the present work will focus on second-order methods, we expect that more accurate finite volume methods will migrate into commercial CFD solvers, and we will plan for a clear upgrade path to providing adaptation and robustness improvements for high order methods in the five to ten year time frame.These advances will provide an important competitive advantage to our industrial partner in this project, ANSYS Canada, as the vendor whose software will be the first to provide these capabilities. In turn, their Canadian customers will benefit through improved accuracy of and confidence in simulation results and increased productivity of engineers using CFD.