Many modeling studies have been completed by the Sanders group over years. Most of these focus on Godunov-based finite volume schemes proposed or used to solve 1D and 2D flow equations of interest to hydraulic engineers. Here is a brief synopsis of model-development studies completed by the Sanders group:

1)     Cross-sectionally integrated (1D) flow and transport models. Sanders (2001) presents a Godunov-based finite volume scheme applicable to non-prismatic channels with triangular or trapezoidal cross-sections. Here, Roe’s Riemann solver is adapted to non-rectangular channels and a discretization of the non-prismatic source term is proposed. Sanders et al. (2001) presents an extension of this scheme to networks of 1D channels, and a nested 2D scheme is used to model channel junctions. Sanders et al. (2003) presents a further study on the treatment of bed slope and non-prismatic source terms in 1D. Readers interested in this topic are also advised to read Capart et al. (ASCE Journal of Hydraulic Engineering, 129(5) 2003), which addresses channels of arbitrary cross-section.

2)      Depth-integrated (2D) flow and transport models based on quadrilateral cells. Brett Sanders and Scott Bradford benefited from excellent instruction as graduate students at the University of Michigan, particularly free-surface flow courses taught by Nik Katopodes and computational courses taught by Bram van Leer and Phil Roe. Our first high-resolution shallow-water codes were independently developed as class projects in the 1994-1997 time frame, first by Bradford (PhD in 96) and later by Sanders (PhD in 97). Publications on this subject appeared several years later, one by Bradford and Katopodes (ASCE J. Irrigation and Drainage Engineering, 127(4), 2001) that focused on basin irrigation and another by Bradford and Sanders (2002) that focused on wetting and drying with uneven terrain. Arega and Sanders (2004) presented a Godunov-based scheme as the basis of a tidal flow and transport model, emphasizing the ability of the scheme to validate using physically realistic and consistent flow resistance and dispersion parameters. In Bradford and Sanders (2005), a comparison of many different methods to deal with uneven terrain, including source term upwinding, is presented. In Sanders and Bradford (2006),, analysis of non-linear slope limiters is presented in the context of flow and transport accuracy in problems involving both advective and diffusive terms.  And in Begnudelli and Sanders (2007a), a new method to account for wetting and drying is presented which is particularly beneficial for coupled simulations of scalar transport.

3)      Depth-integrated (2D) flow and transport models based on triangular cells. Begnudelli and Sanders (2006) present an unstructured grid model for flow and transport based on triangular cells, and introduce a new geometric model to account for wetting and drying. Begnudelli and Sanders (2007b) present an application of the model to simulate the St. Francis dam-break flood of 1928 and provide a critical review of the modeling methodology from a predictive standpoint. Begnudelli, Sanders and Bradford (2008) compare the performance of Godunov-based schemes that are formally first- and second-order accuracy, and identify a unique scheme that is formally first-order accurate but achieves close to second order accuracy by leveraging a second-order description of terrain and implementing an adaptive method of variable reconstruction. Sanders (2008) presents a new time stepping scheme that further improves model efficiency, reducing run-times by 50-70%. An executable version of this code can be downloaded from this site.


St. Francis Dam-Break Flood

Simulation of St. Francis flood which occurred in Los Angeles and Ventura Counties in March of 1928. See paper by Begnudelli and Sanders (2007b) for a complete description. 3 MB WMV File 3 MB WMV File

Ka Loka Dam-Break Flood

Simulation of the dam-break flood that occurred Tuesday, March 14, 2006 on the Hawaiian island of Kauai following failure of an earthen dam supporting Ka Loko reservoir. 2 MB WMV File 1 MB WMV File 10 MB AVI File. 20 MB AVI File. 5.4 MB FLASH File JPEG IMAGE The simulation shows the path and timing of flood waters that moved north across Kuhio Highway and into Kilauea Bay. According to the model, the flood wave moved at a speed of 15-20 miles per hour with a depth as large as 20 feet within narrow canyons close to Ka Loka, and at a speed of 5-10 miles per hour with a depth of 10 ft on flatter terrain closer to Kuhio Highway. In addition, the model shows that there would have been little time to evacuate even if failure was immediately detected. The flood wave reached Kuhio Highway 16 minutes after the dam failed, according to the computer model. This model simulation was carried out using the numerical method described by Begnudelli and Sanders (2006).

Reach-Scale Hydrodynamics

In this application of the triangular grid model, a steady volumetric flow rate is specified at the upstream boundaries of an initially dry river bed. A wetting front advances downstream and the model prediction ultimately approaches a steady state.
Plan view animation (500 KB Shockwave File).  Three dimensional animation (1.8 MB Shockwave File).

Hypothetical Dam-Break Simulation

In this application of the triangular grid model, a hypothetical dam is instantaneously removed at the instant the simulation begins. The model predicts the ensuing flood of water through canyon terrain. Boundaries of the model grid correspond to steep canyon walls. (The "canyon" geometry actually corresponds to Newport Bay, California)
Plan view animation (700 KB Shockwave File). Three dimensional animation (2.9 MB Shockwave File).
Three dimensional animation showing grid (3.0 MB Shockwave File).  

Hypothetical Tsunami Runup

Tsunami runup and overland flow simulation. In this application of the triangular grid model, a set of long waves approach a hypothetical island and the model predicts the resulting flooding.
Plan view animation (1.2 MB Shockwave File). Three dimensional animation (3.1 MB Shockwave File).

Impact of Limiters on Flow

Tidal circulation prediction highlighting the effect of limiters. In this application of the quadrilateral grid model, circulation resulting from a 1 m amplitude M2 tide ispredicted for one cycle using two different limiters: Minmod (600 KB Shockwave File) and Superbee (900 KB Shockwave File). Superbee predicts spurious vortical structures. See paper by Sanders and Bradford (2006).