Numerical discretisation of hyperbolic systems of moment equations describing sedimentation in suspensions of rod-like particles

• Published in: Journal of computational physics 2024-09, Vol.513, p.113162, Article 113162
• Main Authors: Dahm, Sina, Giesselmann, Jan, Helzel, Christiane
• Format: Article
• Language: English
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2024.113162

We present a numerical discretisation of the coupled moment systems, previously introduced in Dahm and Helzel [1], which approximate the kinetic-fluid model by Helzel and Tzavaras [2] for sedimentation in suspensions of rod-like particles for a two-dimensional flow problem and a shear flow problem. We use a splitting ansatz which, during each time step, separately computes the update of the macroscopic flow equation and of the moment system. The proof of the hyperbolicity of the moment systems in [1] suggests solving the moment systems with standard numerical methods for hyperbolic problems, like LeVeque's Wave Propagation Algorithm [3]. The number of moment equations used in the hyperbolic moment system can be adapted to locally varying flow features. An error analysis is proposed, which compares the approximation with 2N+1 moment equations to an approximation with 2N+3 moment equations. This analysis suggests an error indicator which can be computed from the numerical approximation of the moment system with 2N+1 moment equations. In order to use moment approximations with a different number of moment equations in different parts of the computational domain, we consider an interface coupling of moment systems with different resolution. Finally, we derive a conservative high-resolution Wave Propagation Algorithm for solving moment systems with different numbers of moment equations. •We present a numerical method for the approximation of a kinetic-fluid model describing sedimentation in suspensions of rod-like particles.•We approximate the high dimensional kinetic model with lower dimensional hyperbolic systems of moment equations.•The number of moment equations can be adapted to account for locally varying flow features.•An error analysis is proposed, which compares the approximation with 2N+1 moment equations to an approximation with 2N+3 moment equations.•The analytical results suggest an error indicator which can be computed from the numerical approximation with 2N+1 moment equations.•Finally, an interface coupling is proposed which couples approximations with different resolution.