Conference: Mathematical models and numerical methods for multiphysics problems

多物理场问题的数学模型和数值方法会议将于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。会议旨在汇集来自不同社区的专家，这些社区采用了多物理场系统的计算模型。多物理场系统模拟两种或多种介质之间的物理相互作用，例如流体流动的耦合、刚性或可变形的多孔介质以及弹性结构。典型的例子有自由流体与多孔介质流动的耦合、流体-结构相互作用、流体-孔隙-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、通过断裂或变形的含水层或水库的流体流动、土壤结构的演变、动脉流动、活体组织的灌注和器官建模，如心脏、肺和脑。会议上展示的工作将涵盖严格的数学和数值分析以及对前沿问题的应用。描述感兴趣的多物理场系统的数学模型由偏微分方程的复杂系统的耦合组成。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，以及孔隙弹性的Biot方程。不同区域发生的物理现象通过运动和动态界面条件进行耦合。建模和仿真过程包括数学模型的完备性分析，稳定、准确和鲁棒的数值方法的设计和分析，以及有效解决策略的开发。尽管近年来取得了重大进展，但这三个领域仍然存在许多挑战。例如，在数学建模方面，耦合设置下Navier Stokes方程中的非线性平流项、非线性全耦合流动输运模型、非线性扩散、迁移率和弹性参数以及非等温效应；在数值方面，采用结构保持和参数鲁棒离散化方法、后验误差估计和网格空间和时间自适应、多尺度和降阶模型；在解方面，有稳定的高阶松耦合时间分裂方法、域分解方法、参数鲁棒单片解算器和预调节器。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讨论最新成果和趋势的环境，并鼓励未来的合作和研究方向。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，认为值得支持。

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.