Numerical algorithms for higher-order accurate discretizations of flows on deforming domains

变形域上流动高阶精确离散的数值算法

• 批准号: RGPIN-2015-05606
• 负责人: Rhebergen, Sander
• 金额: $ 1.38万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=743691
• 关键词: Numerical; algorithms; higher; order; accurate

Canada is one of the largest producers of hydro and wind energy in the world. Optimally designed marine and wind turbine blades can further increase the production of these sources of renewable energy. More than two hundred floods have occurred in Canada over the past century taking many lives and causing billions of dollars in damage. An accurate prediction of flood plains when rivers overflow may prevent the loss of lives and help protect Canadian homes and businesses. These are just two applications that benefit tremendously from computer simulation tools. The success of these simulation tools, however, depends on the implemented algorithms. In this project we will develop new algorithms for more efficient and more accurate simulation tools.Recently we introduced a new class of higher-order accurate algorithms for fluid flows on domains with small deformations. This class has the potential of being more accurate and more efficient than many other numerical methods. Many flow simulations, however, require algorithms that can cope with fluid flows on domains with large deformations. Example of such large deformations include: topological changes in which the domain may split into several sub-domains (e.g. coalescence and break-up of bubbles in boiling processes) and flow around rotating components (e.g. in the design of marine or wind turbines). The overarching objective of the proposed research is to develop the methodology needed for simulating fluid flow on domains with large deformations, building upon our higher-order accurate algorithms.The proposed research benefits Canada by developing algorithms for next generation simulation tools. These tools will enable simulation of a wide variety of flows for applications in industry, environment and society. These applications may include: increasing the production of renewable energy through the design of optimal marine and wind turbine blades; predicting flood plains in the event of rivers overflowing due to extensive rainfall or snow-melt run-off; and predicting blood flow in artificial heart valves. Furthermore, the proposed research will train highly qualified personnel with the critical skills needed to develop and implement accurate numerical methods. This skill-set is essential for software development in Canada as it is widely believed that higher-order numerical methods will soon become the standard in simulation software.

加拿大是世界上最大的水力和风能生产国之一，优化设计的海洋和风力涡轮机叶片可以进一步提高这些可再生能源的产量，在过去的一个世纪里，加拿大发生了两百多次洪水，造成了许多损失。河流泛滥时对洪泛区的准确预测可以防止人员伤亡，并有助于保护加拿大的家庭和企业。这只是计算机模拟工具的两个应用。然而，这些仿真工具的成功取决于所实施的算法，在这个项目中，我们将为越来越精确的仿真工具开发新算法。最近，我们引入了一类新的高阶精确算法，用于小域上的流体流动。然而，此类具有比许多其他数值方法更准确、更高效的潜力，需要能够处理大型域上的流体流动的算法。此类大变形的示例包括：拓扑变化，其中域可能分裂成多个子域（例如，沸腾过程中气泡的合并和破裂）以及旋转部件周围的流动（例如，在船舶或风力涡轮机的设计中）。 ）所提出的研究的总体目标是开发模拟大变形域中的流体流动所需的方法，以我们的高阶精确度为基础。拟议的研究通过开发下一代模拟工具的算法使加拿大受益，这些工具将能够模拟工业、环境和社会中的各种应用。这些应用可能包括：通过设计增加可再生能源的产量。优化海洋和风力涡轮机叶片；预测由于大量降雨或融雪径流而导致河流泛滥的情况；并预测人工心脏瓣膜中的血流。拟议的研究将培养具有开发和实施精确数值方法所需关键技能的高素质人才，这种技能对于加拿大的软件开发至关重要，因为人们普遍认为高阶数值方法将很快成为模拟领域的标准。软件。