## 1. Introduction

[2] Water flow and sediment transport are simultaneous and interactive processes in rivers, floodplains, and coastal areas. The interaction among these processes is influenced by both human activities and extreme natural events, resulting in aggradation and degradation in channels and harbors, deterioration of water quality and fisheries among other environmental effects, and many other forms of ecological disturbance. Examples include dam removal, dam break, and extreme storm events that induce rapidly varying flow and sediment flushing. The disturbance is complex because of the uneven and changing bottom topography, irregular boundaries, rapid and strong erosion with abrupt bed and flow variations, and complicated and uncertain flow-sediment transport mechanisms. Under these conditions, one-dimensional, uncoupled strategies are generally not sufficient, and two-dimensional approaches capable of handling complicated geometry, rapidly varying flow, and fully coupled physics are necessary. This research builds on recent advances for numerical solutions to fully coupled multiphysics problems in engineering and computational fluid dynamics to flow, sediment, and bed morphology interaction in rivers and tests the model over a range of scales in laboratory and field experiments.

[3] The shallow water equations are typically used to represent the hydrodynamics of river floods, storm surges, tidal fluctuations, tsunami waves, and forces acting on offshore structures [*Aizinger and Dawson*, 2002]. Methods for solving the shallow water equations include the method of characteristics [e.g., *Katopodes and Strelkoff*, 1978], finite difference [e.g., *Molls and Chaudhry*, 1995], finite element [e.g., *Hervouet*, 2000], and finite volume [e.g., *Alcrudo and Garcia-Navarro*, 1993; *Zhao et al.*, 1994; *Anastasiou and Chan*, 1997; *Sleigh et al.*, 1998; *Toro*, 2001; *Bradford and Sanders*, 2002; *Valiani et al.*, 2002; *Yoon and Kang*, 2004; *Begnudelli and Sanders*, 2006]. Although each method has its own strengths and limitations, it is generally true that unstructured grids have advantages for representing natural channels. An algorithm for “optimal” unstructured grids was proposed by *Shewchuk* [1997], which is able to provide an “optimal” representation of the domain with the least number of elements while still conforming to a limited set of physical and geometric constraints particular to the physical domain.

[4] With respect to the numerical method, the finite volume method allows for local and global mass conservation, can be applied to structured or unstructured grids, and requires less memory for explicit calculations as compared to finite difference or finite element methods [*Loukili and Soulaimani*, 2007]. Several investigators have solved the shallow water equations on unstructured grids using finite volume methods [*Zhao et al.*, 1994; *Anastasiou and Chan*, 1997; *Sleigh et al.*, 1998; *Yoon and Kang*, 2004], although sediment transport was not considered in those models. The coupled behavior of sediment transport and bed elevation changes was experimentally studied by *Capart and Young* [1998], with implications for the dynamics of the flow regime as well. For coupled sediment transport and bed evolution the assumption of nonequilibrium conditions enforces a dynamic exchange between sediment deposition and entrainment, and this coupling is explored in this paper.

[5] Relatively few models and fewer field observations are available to study 2-D coupled hydrodynamic flow and sediment transport. An example is a large flood event or dam break on an initially dry surface where full water–sediment–bed form coupling is likely to be important. The dry-to-wet transition followed by a wet-to-dry transition with an evolving bed surface during postevent relaxation produces interesting multiscale behavior. Recently, several 1-D models were developed to simulate the dam-break-induced sediment transport or high-concentration sediment transport as in hyperconcentrated flow and debris flow [*Bellos and Hrissanthou*, 1998; *Fraccarollo et al.*, 2003; *Cao et al.*, 2004; *Ottevanger*, 2005; *Rosatti and Fraccarollo*, 2006; *Wu and Wang*, 2007]. *Hudson and Sweby* [2003] and *Castro Diaz et al.* [2008] discussed 1-D bed load transport models coupled with shallow water equations by finite volume methods. A few studies were found in the 2-D case. *Hudson and Sweby* [2005] and *Simpson and Castelltort* [2006] extended the 1-D models of *Hudson and Sweby* [2003] and *Cao et al.* [2004] to 2-D on structured grids, although the models were not tested in laboratory experiments or real flow fields in the field. *Liu et al.* [2008] developed a 2-D model of shallow water equations and bed load transport. Delft3D is capable of modeling 2-D and 3-D hydrodynamics and sediment transport using a finite difference method (http://delftsoftware.wldelft.nl/). Neither of these models considered the effects of suspended sediment on the hydrodynamics.

[6] In this paper we present a strategy for numerical solution of the system of fully coupled partial differential equations for 2-D shallow water flow, sediment transport, and bed evolution. We test the code against published laboratory, field, and numerical experiments to demonstrate the multiscale performance of the model. The model, referred to as PIHM_Hydro, is based on a cell-centered upwind finite volume method using Roe's approximate Riemann solver on an unstructured triangular grid. A multidimensional linear reconstruction technique and multidimensional slope limiter [*Jawahar and Kamath*, 2000] are implemented to achieve a second-order spatial accuracy. For model efficiency and stability, an explicit-implicit method is used in temporal discretization with operator splitting where advection and nonstiff source terms are solved via an explicit scheme with the stiff source terms handled by a fully implicit scheme. A number of test cases over a range of spatial scales and hydrological events are used to test the model and demonstrate the potential application. The code is open source and available from the authors.