Volume 4, Issue 4
Continuous Sedimentation in Clarifier-Thickener Units: Modeling Macroscopic Conservation Laws from M

NADINE BRAXMEIER-EVEN AND CHRISTIAN KLINGENBERG

Int. J. Numer. Anal. Mod. B, 4 (2013), pp. 372-381

Published online: 2013-04

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  • Abstract
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.
  • AMS Subject Headings

35L60 60K35 82C22

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@Article{IJNAMB-4-372, author = {NADINE BRAXMEIER-EVEN AND CHRISTIAN KLINGENBERG}, title = {Continuous Sedimentation in Clarifier-Thickener Units: Modeling Macroscopic Conservation Laws from M}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {4}, pages = {372--381}, abstract = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/263.html} }
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.
NADINE BRAXMEIER-EVEN AND CHRISTIAN KLINGENBERG. (1970). Continuous Sedimentation in Clarifier-Thickener Units: Modeling Macroscopic Conservation Laws from M. International Journal of Numerical Analysis Modeling Series B. 4 (4). 372-381. doi:
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