Volume 25, Issue 3
Moment Approximations and Model Cascades for Shallow Flow

Julia Kowalski & Manuel Torrilhon

Commun. Comput. Phys., 25 (2019), pp. 669-702.

Published online: 2018-11

Preview Full PDF 128 1490
Export citation
  • Abstract

Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates depthaveraging. While the shallow flow formulation is advantageous in terms of computational efficiency, it also comes at the price of losing vertical information such as the flow’s velocity profile. This gives rise to a model error, which limits the shallow flow model’s predictive power and is often not explicitly quantifiable. We propose the use of vertical moments to overcome this problem. The shallow moment approximation preserves information on the vertical flow structure while still making use of the simplifying framework of depth-averaging. In this article, we derive a generic shallow flow moment system of arbitrary order starting from a set of balance laws, which has been reduced by scaling arguments. The derivation is based on a fully vertically resolved reference model with the vertical coordinate mapped onto the unit interval. We specify the shallow flow moment hierarchy for kinematic and Newtonian flow conditions and present 1D numerical results for shallow moment systems up to third order. Finally, we assess their performance with respect to both the standard shallow flow equations as well as with respect to the vertically resolved reference model. Our results show that depending on the parameter regime, e.g. friction and slip, shallow moment approximations significantly reduce the model error in shallow flow regimes and have a lot of potential to increase the predictive power of shallow flow models, while keeping them computationally cost efficient.

  • Keywords

Shallow flow moment approximation hyperbolic systems.

  • AMS Subject Headings

76D05 35L65 65M08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-25-669, author = {Julia Kowalski and Manuel Torrilhon}, title = {Moment Approximations and Model Cascades for Shallow Flow}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {669--702}, abstract = {

Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates depthaveraging. While the shallow flow formulation is advantageous in terms of computational efficiency, it also comes at the price of losing vertical information such as the flow’s velocity profile. This gives rise to a model error, which limits the shallow flow model’s predictive power and is often not explicitly quantifiable. We propose the use of vertical moments to overcome this problem. The shallow moment approximation preserves information on the vertical flow structure while still making use of the simplifying framework of depth-averaging. In this article, we derive a generic shallow flow moment system of arbitrary order starting from a set of balance laws, which has been reduced by scaling arguments. The derivation is based on a fully vertically resolved reference model with the vertical coordinate mapped onto the unit interval. We specify the shallow flow moment hierarchy for kinematic and Newtonian flow conditions and present 1D numerical results for shallow moment systems up to third order. Finally, we assess their performance with respect to both the standard shallow flow equations as well as with respect to the vertically resolved reference model. Our results show that depending on the parameter regime, e.g. friction and slip, shallow moment approximations significantly reduce the model error in shallow flow regimes and have a lot of potential to increase the predictive power of shallow flow models, while keeping them computationally cost efficient.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0263}, url = {http://global-sci.org/intro/article_detail/cicp/12825.html} }
Copy to clipboard
The citation has been copied to your clipboard