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

TLDR: The results point to mesh-type tradeoffs that should be considered in flood modeling applications, and 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.

About: This article is published in Advances in Water Resources.The article was published on 2014-06-01 and is currently open access. It has received 88 citations till now. The article focuses on the topics: Grid & Unstructured grid.

Figures

Table 1 Properties of meshes, run times and L1 norms for classical dam-break problem.

Fig. 1. Comparison of water depth predictions and exact solutions for classical dam-break problem in a (a) dry bed and (b) wet bed.

Fig. 3. Five mesh types for uniform flow test case. (a) Unconstrained Cartesian grid, (b) Unconstrained Delaunay mesh, (c) Constrained Cartesian grid, (d) Constrained Delaunay grid and (e) Constrained right-triangle grid (unit: m).

Fig. 2. Errors in classical dam-break water depth predictions versus run times in a (a) dry bed and (b) wet bed.

Fig. 10. Comparison of water depth predictions and measurements for aligned blocks in Toce valley test case.

Fig. 16. Comparison of flood arrival time predictions based on (a) shutdown time of electric transformers, (b) gage measurements at physical model.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Mesh type tradeoffs in 2d hydrodynamic modeling of flooding with a godunov-based flow solver" ?

The effect of mesh type on the accuracy and computational demands of a two-dimensional Godunov-type flood inundation model is critically examined. 

Q2. What is the mesh type used in the study?

Three mesh types are examined including a Cartesian grid, a constrained Delaunay mesh (triangular grid), and a mixed mesh of triangular and quadrilateral cells. 

Q3. What are the main factors in the modeling of floods?

Two other important considerations in flood modeling include model selection, which bears on structural model errors, and the demands of model set up and parameterization. 

Q4. What is the advantage of unstructured meshes?

in applications involving natural topography and irregular domain boundaries, there is a benefit to localized refinement in terms of reducing both input data errors (better sampling of topography) and reducing numerical errors, and in this context the unstructured mesh designs prove advantageous. 

Q5. What is the way to predict flood heights?

Previous studies suggest topographic and hydrologic errors are generally greater than numerical errors in flood prediction models [6], and results here also indicate that numerical errors may be negligible, compared to structural model errors and input data errors, for the purpose of predicting maximum flood heights. 

Q6. What is the goal of the Malpasset dam-break flood?

Field-scale performance is the ultimate goal of flood inundation models, and here attention turns to the Malpasset dam-break flood which is one of the most-studied historical events from a 2D modeling perspective [16,34,40,46,50,51,69,77,84]. 

Q7. What is the example of a mesh that can be used to reduce numerical errors?

in rectangular channel geometries, a uniform resolution mesh works well so unstructured meshing capabilities (localized refinement) are not advantageous. 

Q8. What is the impact of LTS on runtimes?

The impact of LTS on runtimes is greater for the unstructured meshes (factor of 2–3 change) than the Cartesian grid (less than 30% change). 

Q9. What is the topography data used in previous studies?

Topography data used in previous modeling studies is also used here, and consists of a digitized set of 13,541 points taken from a historical 1:20,000 scale topographic map and spaced from 6 to 450 m apart [36]. 

Q10. Why is there no optimal mesh type for flood modeling?

There is no optimal mesh type for flood modeling with Godunov-type shallow-water models, because each element type (e.g., triangle and quadrilateral) is advantageous under different circumstances. 

Q11. What was the resolution for the raster DTM?

A 5 m resolution raster DTM was created from these points using the terrain-to-raster tool in ArcGIS (ESRI, Redlands, CA, USA), which was found to be preferable to a TIN structure for representing the channel thalweg. 

Q12. How many meshes were used to parameterize building drag?

To parameterize building drag using Eq. (11), a uniform drag coefficient was used coD ¼ 1Table 4 Properties of meshes, run times for Toce valley test case. 

Q13. What is the way to test the efficiency of a computational hydraulics model?

These classic problems in computational hydraulics test whether a model is capable of resolving trans-critical flows with shocks without spurious oscillations or excessive numerical diffusion. 

Q14. Why is the unstructured meshes better at reducing numerical errors?

This is attributed to the ability of unstructured meshes to locally focus computational resources (local refinement), and the sensitivity of unstructured mesh models to LTS. 

Q15. What is the alternative to a normal mesh?

To summarize, this test problem shows that Cartesian meshes are best suited to modeling flows in prismatic channels, and unconstrained Delaunay meshes represent the least accurate alternative.