Time: February 23, 2026, 14:00
S2 416-2

Titel: Numerical Aspects of Isogeometric Semi-Lagrangian Analysis

Abstract: 
This study presents a unified isogeometric analysis (IgA) based on NURBS (Non-Uniform Rational BSplines) functions. This framework enables an accurate and stable simulation of advection-dominated multiphysic transport problems in biological systems and geophysical flows. The core numerical strategy combines the geometric exactness of IgA with semi-Lagrangian methods and L2-projection techniques to address two key challenges: numerical instability arising from strong advection and the complex coupling of physics. In the context of biological pattern formation (e.g. Schnakenberg-Turing systems), the method employs operator splitting in conjunction with a semi-Lagrangian approach to advection, enabling the precise resolution of the intricate interplay between nonlinear reactions, diffusion and transport, which govern morphogenesis. The L2-projection approach in porous media applications (e.g. miscible displacement with viscous fingering), handles the distortion-prone, dominant convection inherent to Darcy-scale flows, while preserving sharp fronts on complex domains. In both contexts, integrating an exact geometric representation enables large time steps to be taken without compromising accuracy. Numerical results demonstrate the efficacy of the framework in capturing intricate spatiotemporal dynamics, from Turing patterns to fluid mixing interfaces, and highlight the profound influence of domain geometry on solution evolution.

Keywords: Isogeometric Analysis (IgA), Characteristic Galerkin, Transport Problems, Advection-Dominance, Operator Splitting, Turing Patterns, Miscible Displacement, Porous Media, Multiphysic Systems