Structure-Preserving Methods for Complex Fluids

• Applicant: Professorin Dr. Christiane Helzel
• Subject Area: Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 463312734

We construct numerical methods for a system of partial differential equations consisting of a kinetic equation coupled to a macroscopic flow equation, which models sedimentation in suspensions of rod-like particles. A hierarchy of moment equations will be derived which approximates the high-dimensional scalar kinetic equation with a lower dimensional system. The number of moment equations will be adjusted locally based on the dynamics of the problem. This requires an interface coupling of moment systems with different resolution.For the underlying mathematical model thermodynamic consistency can be shown. We will investigate whether this structure can be preserved by the numerical method.This project is part of the DFG research unit "Structure-Preserving Numerical Methods for Bulk- and Interface-Coupling of Heterogeneous Models (SNuBIC)".

• DFG Programme: Research Units
• Subproject of: FOR 5409: Structure-Preserving Numerical Methods for Bulk- and Interface-Coupling of Heterogeneous Models