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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。导电流体（例如，液态金属冷却剂、盐水、离子化气体或等离子体）是重要的，因为它具有许多应用，例如，核反应堆、生产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，流体速度场与磁场之间相互作用的精确数值模拟在计算上也往往具有挑战性、艰巨且昂贵得令人望而却步。这是因为这两个场是非线性耦合的。此外，许多实际的流动发生在对流占主导地位的制度和他们的数值模拟使用标准算法产生数值不稳定性。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，发展高精度的数值算法来模拟这样复杂的问题是非常重要的。首先，这个项目将研究用于模拟不可压缩流动问题（不存在磁场）的有效的系综方案。其次，该项目将专注于理解数值不稳定性，并开发强大，高效和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指导本科生和研究生在数值分析和科学计算方面的研究来实现。该项目的重点是了解Navier-Stokes（N-S）和MHD流模拟的不确定性量化（UQ）中的数值不稳定性。本计画的目标是发展、分析及测试强健且有效率的N-S及MHD流系综模拟新演算法。第一个研究目标是开发和研究一种有效的稳定罚投影有限元法（SPP-FEM）的流体流动模拟的UQ。SPP-FEM以一种优雅的方式提出，在每个时间步，它允许一个共享的系统矩阵，每个实现结合一个稳定的惩罚投影步骤。该格式对于时间步长是无条件稳定的，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适当正交分解（POD）的降阶模型（ROM）稳定的进化-滤波-松弛随机配置ROM（EFR-SCM-ROM）算法，以处理MHD流系UQ ROM中经常出现的数值振荡。EFR-SCM-ROM算法使用随机配置方法（SCM）近似参数的随机性，并使用高阶ROM空间微分滤波器结合演进-然后-滤波-然后-松弛方案来衰减标准ROM的数值振荡。新的EFR-SCM-ROM框架产生精确的近似，最大限度地减少输入数据中的噪声的敏感性，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算法是一种创新的、被认为是新的方法，它将丰富和革命性地改变MHD流系数值近似的计算方法和平台。这些研究将推进MHD流系综领域和其他多物理问题领域的知识基础，包括Boussinesq系统。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。