Adaptive Multiscale Simulation Framework for Reduced-Order Modeling in Perforated Domains

穿孔域降阶建模的自适应多尺度仿真框架

• 批准号: 1620318
• 负责人: Yalchin Efendiev
• 金额: $ 21万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620318&HistoricalAwards=false
• 关键词: Adaptive; Multiscale; Simulation; Framework; Reduced

Processes in perforated domains occur in many important applications. These include complex processes in soil, membranes, and filters. With current imaging techniques, detailed microscale geometries of these perforated materials can be constructed. However, it is prohibitively expensive to solve complex processes in these perforated domains due to a rich hierarchy of scales. For this reason, some types of reduced-order computational techniques are needed. The goal of this project is to develop and analyze novel computational techniques for solving challenging multiscale problems in perforated domains. The new approaches will bring the information from the detailed geometries to large-scale simulations and will improve the predictions in the simulations. This will further allow deigning new materials and optimize processes. Many current approaches for multiscale methods for problems in perforated domains have been restricted to homogenization, which is applicable when the media has scale separation. However, in many realistic perforated media, there is no scale separation, i.e., pore sizes can have a wide variety of scales. The multiscale methods of this project develop a general framework that allows rigorous and systematic reduction. The PI's goals are: (1) to develop systematic local model reduction tools for computing multiscale basis functions; (2) to develop and analyze new finite element techniques using these basis functions; (3) to study the interplay between localization of the basis functions and the global coupling mechanism; (4) to apply the developed methods to a wide variety of flows with nonlinearities and multiphysics in 3D; (5) to test and demonstrate their capabilities for solving problems in engineering and geosciences.

穿孔域中的过程发生在许多重要的应用中。这些包括土壤，膜和过滤器中的复杂过程。使用当前的成像技术，可以构建这些穿孔材料的详细微观几何形状。但是，由于尺度的层次结构，解决这些穿孔域中的复杂过程非常昂贵。因此，需要某些类型的减少计算技术。该项目的目的是开发和分析新颖的计算技术，以解决穿孔域中的挑战性多尺度问题。新方法将将信息从详细的几何形状带到大规模模拟，并将改善模拟中的预测。这将进一步使新材料发放并优化流程。当前许多用于穿孔域问题的多尺度方法的方法都仅限于同质化，这在媒体具有比例分离时适用。但是，在许多现实的穿孔介质中，没有比例分离，即孔径可以具有多种尺度。该项目的多尺度方法开发了一个通用框架，可以进行严格而系统的减少。 PI的目标是：（1）开发用于计算多尺度函数的系统局部模型减少工具； （2）使用这些基础功能开发和分析新的有限元技术； （3）研究基本函数的定位与全局耦合机制之间的相互作用； （4）将开发的方法应用于3D中具有非线性和多物理学的各种流； （5）测试和证明其解决工程和地球科学问题的能力。