Conference: Mathematical models and numerical methods for multiphysics problems

会议：多物理问题的数学模型和数值方法

• 批准号: 2347546
• 负责人: Ivan Yotov
• 金额: $ 3万
• 依托单位: University of Pittsburgh
• 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: 2024-01-15 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2347546&HistoricalAwards=false
• 关键词: Conference; Mathematical; models; numerical; methods

The Mathematical Models and Numerical Methods for Multiphysics Problems Conference is held May 1-3, 2024 at the University of Pittsburgh in Pittsburgh, PA. The conference aims to bring together experts from different communities in which computational models for multiphysics systems are employed. Multiphysics systems model the physical interactions between two or more media, such as couplings of fluid flows, rigid or deformable porous media, and elastic structures. Typical examples are coupling of free fluid and porous media flows, fluid-structure interaction, and fluid-poroelastic structure interaction. Applications of interest include climate modeling, interaction of surface and subsurface hydrological systems, fluid flows through fractured or deformable aquifers or reservoirs, evolution of soil structures, arterial flows, perfusion of living tissues, and organ modeling, such as the heart, lungs, and brain. The work presented at the conference will cover both rigorous mathematical and numerical analysis and applications to cutting-edge problems.The mathematical models describing the multiphysics systems of interest consist of couplings of complex systems of partial differential equations. Examples include the Stokes/Navier-Stokes equations for free fluid flows, the linear or nonlinear elasticity equations for structure mechanics, the Darcy equations for porous media flows, and the Biot equations for poroelasticity. Physical phenomena occurring in different regions are coupled through kinematic and dynamic interface conditions. The modeling and simulation process involves well-posedness analysis of the mathematical models, design and analysis of stable, accurate, and robust numerical methods, and development of efficient solution strategies. Despite significant progress in recent years, many challenges remain in all three areas. Examples include, on the mathematical modeling side, the nonlinear advection term in the Navier Stokes equations in coupled settings, nonlinear fully-coupled flow-transport models, nonlinear diffusion, mobility, and elastic parameters, and non-isothermal effects; on the numerical side, structure preserving and parameter robust discretization methods, a posteriori error estimation and mesh adaptivity in both space and time, multiscale and reduced order models; on the solution side, stable and higher-order loosely-coupled time splitting methods, domain decomposition methods, and parameter-robust monolithic solvers and preconditioners. The conference will bring together experts in the field who are actively working to address these challenges. It will provide an environment for them to discuss state-of-the-art results and trends and encourage future collaborations and research directions. The conference website is https://www.mathematics.pitt.edu/events/mathematical-models-and-numerical-methods-multiphysics-systemsThis 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.

多物理场问题的数学模型和数值方法会议于2024年5月1日至3日在宾夕法尼亚州匹兹堡的匹兹堡大学举行。该会议旨在汇集来自不同社区的专家，其中采用了多物理场系统的计算模型。多物理场系统对两种或多种介质之间的物理相互作用进行建模，例如流体流动、刚性或可变形多孔介质和弹性结构的耦合。典型的例子是自由流体和多孔介质流动的耦合，流体-结构相互作用，以及流体-多孔弹性结构相互作用。感兴趣的应用包括气候建模，地表和地下水文系统的相互作用，通过断裂或变形含水层或水库的流体流动，土壤结构的演变，动脉流动，活组织的灌注和器官建模，如心脏，肺和大脑。在会议上提出的工作将涵盖严格的数学和数值分析和应用到尖端问题。描述感兴趣的多物理场系统的数学模型由复杂的偏微分方程系统的耦合组成。例子包括自由流体流动的Stokes/Navier-Stokes方程、结构力学的线性或非线性弹性方程、多孔介质流动的Darcy方程和多孔弹性的毕奥方程。不同区域的物理现象通过运动学和动力学界面条件耦合起来。建模和仿真过程涉及数学模型的适定性分析，稳定，准确和鲁棒的数值方法的设计和分析，以及有效的解决方案策略的开发。尽管近年来取得了重大进展，但在所有三个领域仍然存在许多挑战。在数学建模方面，实例包括耦合设置中的Navier Stokes方程中的非线性平流项、非线性完全耦合流动-传输模型、非线性扩散、流动性和弹性参数以及非等温效应;在数值方面，结构保持和参数鲁棒离散化方法，后验误差估计和空间和时间上的网格自适应，多尺度和降阶模型;在解决方案方面，稳定和高阶松耦合时间分裂方法，区域分解方法，参数鲁棒单片求解器和预处理器。会议将汇集该领域的专家，他们正在积极努力应对这些挑战。它将为他们提供一个环境，讨论最先进的结果和趋势，并鼓励未来的合作和研究方向。会议网站是https://www.mathematics.pitt.edu/events/mathematical-models-and-numerical-methods-multiphysics-systemsThis奖反映了NSF的法定使命，并已被认为值得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的支持。