Conference: Mathematical models and numerical methods for multiphysics problems

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

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-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.