TY - JOUR
T1 - Continuous Sedimentation in Clarifier-Thickener Units: Modeling Macroscopic Conservation Laws from M
AU - NADINE BRAXMEIER-EVEN AND CHRISTIAN KLINGENBERG
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 372
EP - 381
PY - 2013
DA - 2013/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/263.html
KW - hyperbolic conservation laws
KW - discontinuous flux functions
KW - hydrodynamic limits
KW - microscopic particle systems
AB - We study a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value
problem for a one-dimensional scalar conservation law with a flux function that depends discontinuously
on the spatial position.

There exists several entropy conditions related to the same conservation law in the literature giving
rise to uniqueness. The same initial data may give rise to different entropy solutions, depending
on the criteria one selects. This motivated us to derive the PDE together with an entropy condition
as a hydrodynamic limit from a microscopic interacting particle system.We are inclined to
prefer the entropy solution selected by this method. It turns out that this is an entropy condition
suggested by Audusse and Pethame in a different context.