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

基本信息

批准号：
2213274
负责人：
Muhammad Mohebujjaman
金额：
$ 24.82万
依托单位：
Texas A&M International University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-01 至 2024-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2213274&HistoricalAwards=false
关键词：
LEAPS MPS Fast Efficient Novel

项目摘要

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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。电气导体（例如，液态金属冷却剂，盐水，离子化气或等离子体）在磁场中的相对运动很重要，因为它在核反应堆中具有许多应用，例如核反应堆，人造太阳可生产无碳电力，人工心脏，人工心脏，磁性含水动力（MHD）泵和Geomagagnetic Dynameros。即使使用先进的计算设施，流体和磁场速度场与磁场速度场之间的相互作用的准确数值模拟通常在计算上具有挑战性，艰巨且过于昂贵。这是因为两个字段是非线性耦合的。此外，许多实际流动发生在以对流为主的制度中发生，使用标准算法会产生数值不稳定性。输入数据中噪声的存在加剧了这种情况。输入不确定性的参与降低了最终解决方案的准确性。因此，重要的是要开发远程高保真性数值算法来模拟如此复杂的问题。首先，该项目将研究有效的集合方案，以模拟不可压缩的流动问题（不存在磁场）。其次，该项目将集中于理解数值不稳定性，并开发出可靠，有效，准确的算法，以模拟速度和磁场相互作用的复杂流问题。该项目将促进来自代表性不足团体的学生的教学和培训，以从事STEM领域的职业。这将通过支持和监督数值分析和科学计算的本科生和研究生研究来实现。该项目的重点是了解Navier-Stokes（N-S）和MHD流量模拟的不确定性定量（UQ）中的数值不稳定性。该项目的目的是开发，分析和测试N-S和MHD流程集合模拟的强大且有效的新型算法。第一个研究目标是为流体流量模拟的UQ开发和研究有效稳定的罚款有限元法（SPP-FEM）。 SPP-FEM以优雅的方式呈现，在每个时间步长，它允许共享系统矩阵，并结合稳定的罚款预测步骤。猜想该方案相对于时间步长无条件稳定，并且比标准数值方法更快，更高的计算效率。第二个研究目标是开发基于正交的分解（POD）减少订单建模（ROM）稳定的Evolve-flove-Relax-Relax随机配置ROM（EFR-SCM-ROM）算法，以处理数值振荡，以通常在MHD流量的ROM中出现的MHD流动量。 EFR-SCM-ROM算法使用随机搭配方法（SCM）近似参数的随机性，并使用高阶ROM空间差异滤波器与进化 - 滤波器（然后是滤波器）相结合，以减轻标准ROM的数值振荡。新的EFR-SCM-ROM框架可得出准确的近似值，最大程度地减少了输入数据中噪声的灵敏度，并使用严格的误差估计来确定实际参数缩放。 SPP-FEM和EFR-SCM-ROM算法是创新的，并且被认为是新颖的方法，它将丰富和彻底改变MHD流程组合数值近似的计算方法和平台。这些研究将推进MHD流程团和其他多物理问题领域的知识库，包括Boussinesq系统。该奖项反映了NSF的法定任务，并认为值得通过基金会的智力优点和更广泛的影响来通过评估来支持。