Volume 29, Issue 1
Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies

Yih-Chin Tai, Jeaniffer Vides, Boniface NkongaChih-Yu Kuo

Commun. Comput. Phys., 29 (2021), pp. 148-185.

Published online: 2020-11

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  • Abstract

This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies. Because the topographic surfaces are generally non-trivially curved, we introduce an appropriate local coordinate system for describing the flow behaviors in an efficient way. The complex surfaces are supposed to be composed of a finite number of triangle elements. Due to the unequal orientation of the triangular elements, the distinct flux directions add to the complexity of solving the Riemann problems at the boundaries of the triangular elements. Hence, a vertex-centered cell system is introduced for computing the evolution of the physical quantities, where the cell boundaries lie within the triangles and the conventional Riemann solvers can be applied. Consequently, there are two mesh scales: the element scale for the local topographic mapping and the vertex-centered cell scale for the evolution of the physical quantities. The final scheme is completed by employing the HLL-approach for computing the numerical flux at the interfaces. Three numerical examples and one application to a large-scale landslide are conducted to examine the performance of the proposed approach as well as to illustrate its capability in describing the shallow flows on complex topographies.

  • Keywords

Multi-mesh-scale approach, complex topography, shallow flows, unstructured mesh, vertex-centered formulation.

  • AMS Subject Headings

35L65, 76M12, 58J90, 86-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-148, author = {Tai , Yih-Chin and Vides , Jeaniffer and Nkonga , Boniface and Kuo , Chih-Yu}, title = {Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {148--185}, abstract = {

This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies. Because the topographic surfaces are generally non-trivially curved, we introduce an appropriate local coordinate system for describing the flow behaviors in an efficient way. The complex surfaces are supposed to be composed of a finite number of triangle elements. Due to the unequal orientation of the triangular elements, the distinct flux directions add to the complexity of solving the Riemann problems at the boundaries of the triangular elements. Hence, a vertex-centered cell system is introduced for computing the evolution of the physical quantities, where the cell boundaries lie within the triangles and the conventional Riemann solvers can be applied. Consequently, there are two mesh scales: the element scale for the local topographic mapping and the vertex-centered cell scale for the evolution of the physical quantities. The final scheme is completed by employing the HLL-approach for computing the numerical flux at the interfaces. Three numerical examples and one application to a large-scale landslide are conducted to examine the performance of the proposed approach as well as to illustrate its capability in describing the shallow flows on complex topographies.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0184}, url = {http://global-sci.org/intro/article_detail/cicp/18426.html} }
TY - JOUR T1 - Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies AU - Tai , Yih-Chin AU - Vides , Jeaniffer AU - Nkonga , Boniface AU - Kuo , Chih-Yu JO - Communications in Computational Physics VL - 1 SP - 148 EP - 185 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0184 UR - https://global-sci.org/intro/article_detail/cicp/18426.html KW - Multi-mesh-scale approach, complex topography, shallow flows, unstructured mesh, vertex-centered formulation. AB -

This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies. Because the topographic surfaces are generally non-trivially curved, we introduce an appropriate local coordinate system for describing the flow behaviors in an efficient way. The complex surfaces are supposed to be composed of a finite number of triangle elements. Due to the unequal orientation of the triangular elements, the distinct flux directions add to the complexity of solving the Riemann problems at the boundaries of the triangular elements. Hence, a vertex-centered cell system is introduced for computing the evolution of the physical quantities, where the cell boundaries lie within the triangles and the conventional Riemann solvers can be applied. Consequently, there are two mesh scales: the element scale for the local topographic mapping and the vertex-centered cell scale for the evolution of the physical quantities. The final scheme is completed by employing the HLL-approach for computing the numerical flux at the interfaces. Three numerical examples and one application to a large-scale landslide are conducted to examine the performance of the proposed approach as well as to illustrate its capability in describing the shallow flows on complex topographies.

Yih-Chin Tai, Jeaniffer Vides, Boniface Nkonga & Chih-Yu Kuo. (2020). Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies. Communications in Computational Physics. 29 (1). 148-185. doi:10.4208/cicp.OA-2019-0184
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