LEAPS-MPS: Fast and Efficient Novel Algorithms for MHD Flow Ensembles

LEAPS-MPS：适用于 MHD 流系综的快速高效的新颖算法

• 批准号: 2425308
• 负责人: Muhammad Mohebujjaman
• 金额: $ 24.82万
• 依托单位: University of Alabama at Birmingham
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2425308&HistoricalAwards=false
• 关键词: LEAPS; MPS; Fast; Efficient; Novel

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The relative movement of an electrically conducting fluid (e.g., liquid metal coolant, saltwater, ionized gases, or plasmas) in a magnetic field is important as it has many applications in, e.g., nuclear reactors, artificial suns to produce carbon-free electricity, artificial hearts, magnetohydrodynamic (MHD) pumps, and geomagnetic dynamos. The accurate numerical simulation of the interaction between the velocity field of the fluid and the magnetic field is often computationally challenging, arduous, and prohibitively expensive even with the use of an advanced computing facility. This is because the two fields are non-linearly coupled. Moreover, many practical flows occur in a convection-dominated regime and their numerical simulations using standard algorithms produce numerical instability. The scenario is exacerbated by the presence of noise in the input data. The involvement of input uncertainties reduces the accuracy of the final solutions. Therefore, it is important to develop long-range high fidelity numerical algorithms for simulating such a complex problem. First, this project will investigate efficient ensemble schemes for simulating incompressible flow problems (without the presence of a magnetic field). Second, this project will focus on understanding the numerical instability and develop robust, efficient, and accurate algorithms for simulating complex flow problems where velocity and magnetic fields interact. This project will facilitate the teaching and training of students from underrepresented groups to pursue their careers in STEM fields. This will be carried out by supporting and supervising undergraduate and graduate students' research in numerical analysis and scientific computing.The focus of this project is to understand the numerical instability in the uncertainty quantification (UQ) of Navier-Stokes (N-S) and MHD flow simulations. The objective of this project is to develop, analyze, and test robust, and efficient novel algorithms of N-S and MHD flow ensembles simulations. The first research goal is to develop and investigate an efficient Stabilized Penalty-projection Finite Element Method (SPP-FEM) for the UQ of fluid flow simulations. The SPP-FEM is presented in an elegant way that at each time-step, it permits a shared system matrix for each realization in conjunction with a stabilized penalty-projection step. It is conjectured that the scheme will be unconditionally stable with respect to the time-step size and would be much faster and more computationally efficient than standard numerical methods. The second research goal is to develop a Proper Orthogonal Decomposition (POD) based Reduced Order Modeling (ROM) stabilized Evolve-Filter-Relax Stochastic Collocation ROM (EFR-SCM-ROM) algorithm to deal with the numerical oscillations, which commonly arise in ROM of the UQ of MHD flow ensembles. The EFR-SCM-ROM algorithm approximates the randomness of the parameters using stochastic collocation methods (SCMs) and uses a high-order ROM spatial differential filter in conjunction with an evolve-then-filter-then-relax scheme to attenuate the numerical oscillations of standard ROMs. The new EFR-SCM-ROM framework yields accurate approximations, minimizes the sensitivity of noise in input data, and uses rigorous error estimates to determine practical parameter scaling. The SPP-FEM and EFR-SCM-ROM algorithms are innovative and considered novel approaches, which will enrich and revolutionize the computational methodology and platform for the numerical approximation of MHD flow ensembles. These studies will advance the knowledge base in the field of MHD flow ensembles and other fields of multi-physics problems, including Boussinesq systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项的全部或部分资金根据《2021 年美国救援计划法案》（公法 117-2）提供。导电流体（例如液态金属冷却剂、盐水、电离气体或等离子体）在磁场中的相对运动非常重要，因为它在核反应堆、产生无碳电力的人造太阳、人造心脏、磁流体动力 (MHD) 泵和地磁发电机。即使使用先进的计算设施，对流体的速度场和磁场之间的相互作用进行精确的数值模拟通常在计算上具有挑战性、艰巨且昂贵。这是因为这两个场是非线性耦合的。此外，许多实际流动发生在对流主导的情况下，并且使用标准算法进行的数值模拟会产生数值不稳定。输入数据中存在噪声会加剧这种情况。输入不确定性的参与降低了最终解决方案的准确性。因此，开发远程高保真数值算法来模拟此类复杂问题非常重要。首先，该项目将研究用于模拟不可压缩流动问题（不存在磁场）的有效系综方案。其次，该项目将重点了解数值不稳定性，并开发稳健、高效且准确的算法来模拟速度和磁场相互作用的复杂流动问题。该项目将促进来自代表性不足群体的学生的教学和培训，以追求他们在 STEM 领域的职业生涯。该项目将通过支持和监督本科生和研究生在数值分析和科学计算方面的研究来进行。该项目的重点是了解纳维-斯托克斯 (N-S) 和 MHD 流的不确定性量化 (UQ) 中的数值不稳定性模拟。该项目的目标是开发、分析和测试稳健且高效的 N-S 和 MHD 流系综模拟的新颖算法。第一个研究目标是开发和研究一种用于 UQ 流体流动模拟的高效稳定惩罚投影有限元方法 (SPP-FEM)。 SPP-FEM 以一种优雅的方式呈现，在每个时间步长，它允许为每个实现提供一个共享系统矩阵以及稳定的惩罚投影步骤。据推测，该方案在时间步长方面将是无条件稳定的，并且比标准数值方法更快、计算效率更高。第二个研究目标是开发一种基于本征正交分解 (POD) 的降阶建模 (ROM) 稳定演化-滤波器-松弛随机搭配 ROM (EFR-SCM-ROM) 算法来处理 ROM 中常见的数值振荡MHD 流系综的 UQ。 EFR-SCM-ROM 算法使用随机配置方法 (SCM) 来近似参数的随机性，并使用高阶 ROM 空间微分滤波器结合演化-然后-滤波-然后-松弛方案来衰减标准 ROM。新的 EFR-SCM-ROM 框架可产生精确的近似值，最大限度地降低输入数据中噪声的敏感性，并使用严格的误差估计来确定实际的参数缩放。 SPP-FEM 和 EFR-SCM-ROM 算法是创新的，被认为是新颖的方法，它将丰富和彻底改变 MHD 流系综数值逼近的计算方法和平台。这些研究将推进 MHD 流系综领域和其他多物理问题领域（包括 Boussinesq 系统）的知识基础。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响进行评估，被认为值得支持审查标准。