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

随着计算机能力的增强，使用计算流体动力学(CFD)模拟问题的复杂性也迅速增长。此外，还更加重视量化模拟结果的准确性。用于该任务的现有技术通常具有令人望而却步的巨大计算资源需求。 满足这一需求需要一种新的范例，在这种范例中，具有自适应和误差量化能力的健壮的流动解算器能够可靠地产生具有已知误差界限的解决方案，并且只需最少的人工干预。该项目将原型新的技术，以估计和减少流动问题模拟中的数值误差，并使商业CFD软件更有效，能够更强大地计算解决方案。我们将在一个与现代商业CFD解算器中使用的二阶非结构网格有限体积方法兼容的统一框架下进行这项工作。我们预计，在两到五年内，这些进步可以开始在当前的商业CFD解算器中部署。我们还将与Ansys加拿大公司合作，评估在我们之前的合作项目中开发的新算法与他们现有的商业流动解算器的使用情况。虽然目前的工作将集中在二阶方法上，但我们预计更准确的有限体积方法将移植到商业CFD求解器中，我们将计划在五到十年的时间框架内提供一条明确的升级路径，以提供高阶方法的适应性和健壮性改进。 这些进展将为我们在该项目中的工业合作伙伴--加拿大的Ansys公司提供重要的竞争优势，因为该公司的软件将是第一个提供这些功能的供应商。反过来，他们的加拿大客户将从提高模拟结果的准确性和信心以及提高使用CFD的工程师的生产率中受益。

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.