Soumendra Nath Kuiry

Coupled 1D–quasi-2D flood inundation model with unstructured grids

A simplified numerical model for simulation of floodplain inundation resulting from naturally occurring floods in rivers is presented. Flow through the river is computed by solving the de Saint Venant equations with a one-dimensional (1D) finite volume approach. Spread of excess flood water spilling overbank from the river onto the floodplains is computed using a storage cell model discretized into an unstructured triangular grid. Flow exchange between the one-dimensional river cells and the adjacent floodplain cells or that between adjoining floodplain cells is represented by diffusive-wave approximated equation. A common problem related to the stability of such coupled models is discussed and a solution by way of linearization offered. The accuracy of the computed flow depths by the proposed model is estimated with respect to those predicted by a two-dimensional (2D) finite volume model on hypothetical river-floodplain domains. Finally, the predicted extent of inundation for a flood event on a stretch of River Severn, United Kingdom, by the model is compared to those of two proven two-dimensional flow simulation models and with observed imagery of the flood extents.

A hybrid finite-volume/finite-difference scheme for one-dimensional Boussinesq equations to simulate wave attenuation due to vegetation

A numerical scheme is developed to solve the extended one-dimensional Boussinesq equations for wave propagation through vegetated water bodies. The effects of vegetation are added in the source term of the momentum equation in the form of drag force offered by vegetation to the flowing water. The governing equations are then arranged in such a way that a finite-volume method with the HLL Riemann solver is used to discretize the convective part of the equations, while a finite-difference method is used to discretize the remaining terms. The values of the variables at cell face for the use in the local Riemann problem are computed by a fourth-order MUSCL reconstruction method. The bed slope, bed friction, resistance due to vegetation and Boussinesq terms are discretized using centered finite-difference schemes of up to fourth-order accuracy. The unsteady term is discretized by the second-order MUSCL-Hancock scheme. The resulting discretized equations form a tri-diagonal matrix, which is solved efficiently by the Thomas algorithm. The use of Riemann solver makes the model capable of simulating both breaking and non-breaking waves from deep to shallow water regions. The developed model is validated against various experimental observations and demonstrated to be suitable for predicting wave propagation in vegetated water bodies.

Simulation of Storm Surge in the Mississippi Gulf Coast Using an Integrated Coastal Processes Model

This study uses an integrated coastal processes model to simulate hydrodynamics driven by storms, tides, river inflows, and winds in a large-scale domain covering the Mississippi and Louisiana Gulf Coasts. By using existing bathymetric data and DEM topographic data, a high-resolution mesh is generated to represent structures, roads, rivers, barrier islands, and lakes. For study of flooding and inundation of hurricanes in the inland areas of the Mississippi Gulf Coast, the Pearl River and its floodplain are included in the mesh with a detailed river course. Using two synthetic storms, four hurricane scenarios are simulated by using this model. Computed maximum storm surges without the Pearl River are compared with those with the river inflow. Differences between the storm surges indicate that the inclusion of the river inflow is imperative in order to obtain accurate predictions on flood and inundation due to storm surges in the Mississippi Coast community.

A one-dimensional shock-capturing model for long wave run-up on sloping beaches

This paper presents a one-dimensional finite-volume model to investigate long wave run-up under non-breaking and breaking conditions. A conservative form of the non-linear shallow water equations is solved using a high-resolution Godunov-type scheme coupled with the HLL Riemann solver. The surface gradient method leads to a well-balanced formulation between the flux and the source terms. The explicit time discretisation is first-order accurate, but a piecewise linear reconstruction of numerical data at cell interfaces helps achieve second-order accuracy in space. The computed surface elevation, flow velocity and run-up show very good agreement with available analytical solutions and experimental observations. The model accurately describes propagation of non-breaking and breaking waves on a sloping beach.

APPLICATION OF THE 1D-QUASI 2D MODEL TINFLOOD FOR FLOODPLAIN INUNDATION PREDICTION OF THE RIVER THAMES

ABSTRACT TINFLOOD, a simplified numerical model developed for simulation of floodplain inundation, is applied to predict the extent of flooding at a small reach of the River Thames, UK. River flow is computed by solving the de Saint Venant equations with a one-dimensional finite volume approach. Over-bank flood water spillage from the river onto the floodplains is computed considering mass exchange only between the one-dimensional river cells and the adjacent floodplain cells. Flow exchange between the river and floodplain cells or that between adjoining floodplain cells is represented by a weir type equation. The model employs a linearized form of the flow equation for avoiding instability, common to such coupled models. The rigorously tested model is applied in this study for predicting the extent of inundation for a flood event to a stretch of the River Thames, United Kingdom and compared with the corresponding observed imagery of the flood extents.

A two-dimensional finite volume model for tide and storm surge predictions

An integrated storm surge and inundation modeling system is implemented in an existing software package DSS-WISE TM developed at the National Center for Computational Hydroscience and Engineering. The model is packaged in a GIS based graphical user interface. In the present study, the existing model is enhanced with storm surge prediction capability by including a hurricane track model and some additional forcing terms. The governing equations are discretized by a conservative finite volume method and the HLLC Riemann solver. The topography is defined by Digital Elevation Model and surface roughness can be prescribed based on land use pattern. The wind shear stress is calculated using a parametric wind model. The hurricane pressure field is computed using a hurricane track model by supplying the track of the storm, central pressure, radius of maximum wind and its forward speed. The discretized equations are solved explicitly. The enhanced DSS-WISE TM model is verified by solving analytical tests commonly used for verification study of shallow-water models. The simulation of Hurricane Gustav that made landfall on the Louisiana coast in 2008 is also demonstrated and the preliminary results are analyzed.

Optimal Flood Control in Alluvial Channel Using Adjoint Sensitivity Analysis

Flood flows in alluvial channels (rivers) convey suspended sediments from upstream to downstream, and also entrain bed materials along with flood currents. It is obvious that morphological changes in channels due to sediment deposition/erosion will affect water stages, and results in different hydrographs, in comparison with those in a fixed channel bed. During flood seasons, due to speeding flood currents, even drastic bed changes will occur. It is therefore of importance to take into account morphological changes in alluvial channels induced by flood flows for the purpose of flood control operation. This paper presents a systematical numerical investigation on the effect of morphological change in an alluvial channel on optimal flood control. As an example, the numerical optimal flood control is demonstrated by operating a floodgate to withdraw flood waters from a channel. The optimal withdrawal hydrographs for the floodgate operations are obtained by an integrated numerical optimization modeling system which consists of a hydrodynamic model, a sediment transport model, and a bound constrained optimization model. The hydrodynamic module is to solve the one-dimensional nonlinear de Saint-Venant equations. The sediment transport module solves the non-equilibrium transport equations for non-uniform sediments. And the optimization module is to find the optimal solution iteratively by solving the adjoint equations of the Saint-Venant equations obtained by variational approach. In order to study the effectiveness and applicability of the optimal control theory, alluvial channels with single floodgate is considered for different flow conditions and sediment properties. The changes in morphology due to control of flows are studied thoroughly. It is found that the influence of morphological changes on flood control becomes critical under certain flow conditions and the integrated model is applicable to perform optimal flood control under consideration of sediment transport in alluvial channels/rivers.