A micro-macro hybrid model with application for material and pedestrian flow. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Göttlich, Simone; Pfirsching, Marion
• Editors: Hristov, Jordan
• Is Part Of: Cogent mathematics & statistics. Volume 5:Issue 1(2018)
• Publication Date: 2018-01-01
• Subjects: Microscopic and macroscopic models -- conservation laws with nonlocal flow -- numerical simulation; 82C22 -- 35L65 -- 65M08; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/25742558.2018.1476049
• Languages: English
• ISSNs: 2574-2558

Abstract

Abstract: In this paper, a hybrid modeling approach for granular flow-like applications is presented. The approach allows to switch for a priori fixed points in time between the different levels of description which are the microscopic and macroscopic scale, respectively. Based on the numerical discretization of the models, the switching procedure is able to interpret information on individual objects as density distributions and vice versa. In particular, the reverse direction, i.e. from a macroscopic to a microscopic perspective, requires the solution of a nonlinear least squares problem subject to further constraints. Simulation results are given and demonstrate the good performance of the algorithm in the case of material and pedestrian flow models.