MS159 - Asymptotic-Preserving Schemes and Multiscale Approaches in Biology and and Fluid Dynamics
Keywords: biological network formation, highly oscillatory problems, partial differential equations, uniformly accurate schemes
Understanding complex systems in biology and fluid dynamics often requires the integration of processes across multiple space and time scales. Cellular environments and macroscopic flows are governed by partial differential equations (PDEs); therefore, the development of accurate and efficient multiscale strategies becomes essential. This minisymposium will focus on recent advances in multiscale modeling and simulation, with particular emphasis on applications in biology, chemistry and engineering.
A key theme will be the effective treatment of problems involving multiple interacting scales. In many applications, different levels of details must be combined to capture both local features and global behavior efficiently. This is particularly relevant in systems where geometry, dynamics and material properties vary significantly across scales.
Natural and biological systems often exhibit complex hierarchical structures. For instance, transport networks in living organisms or plants involve branching patterns that span several orders of magnitude, with varying properties at each level. In such cases, adopting a single model across all scales becomes impractical, and specialized techniques are needed to account for the interplay between scales.
Alongside numerical methods, the minisymposium will also address recent theoretical approaches that enhance our understanding of multiscale systems and help ensure that structural and physical properties are respected during modeling and simulation. Topics of interest include Asymptotic-Preserving numerical schemes, mathematical modeling in arbitrary and evolving geometries, and the numerical challenges posed by stiff systems and moving interfaces. The interplay between accuracy, efficiency, and the ability to capture cross-scale behavior will be a central focus.
We invite researchers working in this area to share recent developments and discuss open challenges. Applications of interest include ion transport and sorption across membranes, vascular and plant network formation, flow in fractured or heterogeneous media, and coupled fluid-structure problems in physiological systems.
