Mesh type tradeoffs in 2D hydrodynamic modeling of flooding with a Godunov-based flow solver

Abstract

a b s t r a c tThe effect of mesh type on the accuracy and computational demands of a two-dimensional Godunov-type flood inundation model is critically examined. Cartesian grids, constrained and unconstrained triangular grids, constrained quadrilateral grids, and mixed meshes are considered, with and without local time stepping (LTS), to determine the approach that maximizes computational efficiency defined as accuracy relative to computational effort. A mixed-mesh numerical scheme is introduced so all grids are processed by the same solver. Analysis focuses on a wide range of dam-break type test cases, where Godunov-type flood models have proven very successful. Results show that different mesh types excel under different circumstances. Cartesian grids are 2-3 times more efficient with relatively simple terrain features such as rectilinear channels that call for a uniform grid resolution, while unstructured grids are about twice as efficient in complex domains with irregular terrain features that call for localized refinements. The superior efficiency of locally refined, unstructured grids in complex terrain is attributable to LTS; the locally refined unstructured grid becomes less efficient using global time stepping. These results point to mesh-type tradeoffs that should be considered in flood modeling applications. A mixed mesh model formulation with LTS is recommended as a general purpose solver because the mesh type can be adapted to maximize computational efficiency.

Metric-Resolution 2D River Modeling at the Macroscale: Computational Methods and Applications in a Braided River

“…In meandering rivers with a single channel and relatively flat floodplain, accurate low flow modeling focuses attention on the thalweg and banks of channels and typically dictates the finest resolution adopted by an unstructured grid. Higher flood stages, on the other hand, are typically less demanding (Kim et al, 2014). Braided rivers (BR) are even more demanding to efficiently model because of the range of channel sizes, channel anastomosis, and extensive wetting and drying.…”

“…Macroscale hydrodynamic modeling is also somewhat common with a grid resolution of tens, hundreds or even thousands of meters, sometimes using sub-grid models to account for channel flows (e.g., Neal et al, 2012). Coarsening grid resolution makes hydrodynamic modeling far less demanding because with every doubling of the cell size, run times are reduced by a factor of eight (Kim et al, 2014). Macroscale models may also use a downscaling technique to create the appearance of metric-resolution hydrodynamic modeling after flow calculations are made on a much coarser grid (e.g., Schumann et al, 2014).…”

“…The primary factors affecting the computational demands of hydrodynamic river models are the number of computational cells and time steps required to span the domain and period of interest; computational costs generally scale as the product of these two factors (Kim et al, 2014). For example, a 100 km river reach with a 2 km wide floodplain is spanned by ∼2.0 × 10 8 metric resolution cells.…”

“…Although there are many grid generation tools available, a popular option for triangular grids is Triangle (Shewchuk, 1996), which allows the user to specify constraints on the position of grid vertices and the size of triangles. These features have enabled researchers to systematically use vector data archived in Geographic Information Systems (GIS) to constrain grids generated by Triangle, for example vector data describing building walls (Schubert et al, 2008), roads (Schubert and Sanders, 2012), sea walls (Gallien et al, 2011), channel banks (Kim et al, 2014), and bridge footings (Costabile and Macchione, 2015). These constraints are important not only to vary the spatial resolution of the grid, but also to accurately model channel shape and overtopping thresholds with a relatively coarse (and efficient) computational grid.…”

“…Triangular grids are also referred to as having a Triangular Irregular Network (TIN) data structure (Peucker et al, 1976;Tsai, 1993). Rivers with complex channel networks, islands, and tiered floodplains tend to be good candidates for triangular grids, while systems with relatively simple topography such as engineered channels with regular channel cross-sections are better suited to grids based on quadrilateral cells (Kim et al, 2014). Urban floodplains can present considerable topographic complexity in the form of narrow channels, flood walls, and building walls that affect the movement of flood water, and here triangular grids have proven to be excellent for 2D hydrodynamic modeling (Schubert et al, 2008;Gallegos et al, 2009;Sanders et al, 2010;Gallien et al, 2011;Schubert and Sanders, 2012;Costabile and Macchione, 2015).…”