Jennifer Kötz | Searcharxiv

arXiv2019

Well-posedness of a non-local model for material flow on conveyor belts

In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.

math.AP↗

arXiv2019

Validation of Flow Models as New Simulation Approach for Parcel Handling in Bulk Mode

Flow Models based on hyperbolic partial differential equations (conservation laws) are a well-established approach for the material flow simulation. Until now, they have been exclusively used for the simulation of cylindrical cargo. This paper investigates the application of flow models on cubical cargo as a new simulation approach for parcel logistics. Selected flow model parameters are adapted to cover this new situation. The simulation results of this macroscopic model are compared with the microscopic Discrete Element Method (DEM) where the cargo is approximated by superquadrics. An experimental setup especially designed for the validation of the considered flow model for cubical cargo bulk flow is presented. Results of the flow model are analyzed and validated against the results of experiment and DEM for the test setting.

math.NA↗