Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies (Communications in Computational Physics, 2020)
This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies. Because thetopographic surfaces are generally non-trivially curved, we introduce an appropriatelocal 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. Dueto the unequal orientation of the triangular elements, the distinct flux directions addto the complexity of solving the Riemann problems at the boundaries of the triangularelements. Hence, a vertex-centered cell system is introduced for computing the evolution of the physical quantities, where the cell boundaries lie within the triangles andthe conventional Riemann solvers can be applied. Consequently, there are two meshscales: the element scale for the local topographic mapping and the vertex-centeredcell scale for the evolution of the physical quantities. The final scheme is completed byemploying the HLL-approach for computing the numerical flux at the interfaces. Threenumerical 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 capabilityin describing the shallow flows on complex topographies.