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.
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
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.
Simulation of St. Francis flood which occurred in
Ka Loka Dam-Break Flood
Simulation of the dam-break flood
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
Plan view animation (500 KB Shockwave File). Three dimensional animation (1.8 MB Shockwave File).
Hypothetical Dam-Break Simulation
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
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
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
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
(600 KB Shockwave File) and Superbee (900 KB Shockwave File). Superbee
predicts spurious vortical structures. See paper by Sanders and Bradford (2006).
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