Georges Kesserwani

A 2D shallow flow model for practical dam-break simulations

Dam-break flows usually occur in domains with complex geometric and topographic features and involve abrupt flow patterns. A dam-break model must therefore be able to effectively handle different flow types including transcritical flows or hydraulic jumps, deal with complex domain topography, capture repeating wet–dry interface and represent high roughness values in the floodplain. Herein, all of these objectives are achieved by extending a recent one-dimensional finite volume Godunov-type model into two dimensions for solving the shallow-water equations. While doing so, a much simplified condition to maintain well-balanced solutions around a wet–dry front is proposed and a two-dimensional friction source term discretization is derived under a suitable stability condition in relation to practical simulations. The two-dimensional model is successfully validated against three analytical benchmark tests and then assessed for predicting realistic dam-break flood events.

Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying

This work extends a well-balanced second-order Runge-Kutta discontinuous Galerkin (RKDG2) scheme to provide conservative simulations for shallow flows involving wetting and drying over irregular topographies with friction effects. For this purpose, a wetting and drying technique designed originally for a finite volume (FV) scheme is improved and implemented, which includes the discretization of friction source terms via a splitting implicit integration approach. Another focus of this work is to design a fully conserved RKDG2 scheme to provide conservative solutions for both mass and momentum through a local slope limiting process. Several steady and transient benchmark tests with/without friction effects are simulated to validate the new solver and demonstrate the effects of different slope limiting processes, i.e. globally and locally slope limiting processes.

Topography discretization techniques for Godunov-type shallow water numerical models: a comparative study

This paper compares various topography discretization approaches for Godunov-type shallow water numerical models. Many different approaches have emerged popular with Godunov-type water wave models. To date, literature lacks an investigative study distinguishing their pros and cons, and assessing their reliability relating to issues of practical interest. To address this gap, this work reviews and assesses five standard topography discretization methods that consist of the Upwind, the surface gradient method, the mathematically balanced set of the shallow water equations, the hydrostatic reconstruction technique and the discontinuous Galerkin discretization. The study further considers mix-mode approaches that incorporate wetting and drying in conjunction with the topography discretization. Steady and transient hydraulic tests are employed to measure the performance of the approaches relating to the issues of mesh size, topographys differentiability, accuracy-order of the numerical scheme, and impact of wetting and drying.

Discontinuous Galerkin flood model formulation: Luxury or necessity?

The finite volume Godunov-type flood model formulation is the most comprehensive amongst those currently employed for flood risk modeling. The local Discontinuous Galerkin method constitutes a more complex, rigorous, and extended local Godunov-type formulation. However, the practical merit associated with such an increase in the level of complexity of the formulation is yet to be decided. This work makes the case for a second-order Runge-Kutta Discontinuous Galerkin (RKDG2) formulation and contrasts it with the equivalently accurate finite volume (MUSCL) formulation, both of which solve the Shallow Water Equations (SWE) in two space dimensions. The numerical complexity of both formulations are presented and their capabilities are explored for wide-ranging diagnostic and real-scale tests, incorporating all challenging features relevant to flood inundation modeling. Our findings reveal that the extra complexity associated with the RKDG2 model pays off by providing higher-quality solution behavior on very coarse meshes and improved velocity predictions. The practical implication of this is that improved accuracy for flood modeling simulations will result when terrain data are limited or of a low resolution. Key Points Improved flood model formulation Comparative performance study Implication to flood modeling practice

New Approach for Predicting Flow Bifurcation at Right-Angled Open-Channel Junction

An unsteady mathematical model for predicting flow divisions at a right-angled open-channel junction is presented. Existing dividing models depend on a prior knowledge of a constant flow regime. In addition, their strong nonlinearity does not guarantee compatibility with the St. Venant solutions in the context of an internal boundary condition treatment. Assuming zero crest height at the junction region, a side weir model explicitly introduced within the one-dimensional St. Venant equations is used to cope with the two-dimensional pattern of the flow. An upwind implicit numerical solver is employed to compute the new governing equations. The performance of the proposed technique in predicting super-, trans-, and subcritical flow bifurcations is illustrated by comparing with experimental data and/or theoretical predictions. In all the tests, lateral-to-upstream discharge ratios ( Rq ) are successfully reproduced by the present technique with a maximum error magnitude of less than 9%.

Influence of Total-Variation-Diminishing Slope Limiting on Local Discontinuous Galerkin Solutions of the Shallow Water Equations

Finite volume (FV) slope limiting is essential to stabilize discontinuous Galerkin (DG) solutions despite a number of side effects such as local loss of accuracy and increased run-time cost. These side effects have been experienced with DG solutions to the homogeneous system of conservation laws and are usually accepted as long as they do not affect the reliability of the numerical predictions and provide a better stability property. They have also led to the concept of localizing the slope-limiting process. When a model is applied to simulate the flow problems that necessitate the solution of the inhomogeneous shallow water equations (SWEs) with/without flooding and drying, the slope-limiting routine can have extra adverse effects on the local DG framework. These effects, causes, and implications on DG solutions to the SWEs have not yet received adequate attention, and a full investigation is therefore needed. With the aim of improving a second-order Runge-Kutta discontinuous Galerkin (RKDG2) SWE solver,...

Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations

We provide an adaptive strategy for solving shallow water equations with dynamic grid adaptation including a sparse representation of the bottom topography. A challenge in computing approximate solutions to the shallow water equations including wetting and drying is to achieve the positivity of the water height and the well-balancing of the approximate solution. A key property of our adaptive strategy is that it guarantees that these properties are preserved during the refinement and coarsening steps in the adaptation process.The underlying idea of our adaptive strategy is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. Furthermore we use the multiresolution analysis of the underlying data as an additional indicator of whether the limiter has to be applied on a cell or not. By this the number of cells where the limiter is applied is reduced without spoiling the accuracy of the solution.By means of well-known 1D and 2D benchmark problems, we verify that multiwavelet-based grid adaptation can significantly reduce the computational cost by sparsening the computational grids, while retaining accuracy and keeping well-balancing and positivity.

Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport

A one-dimensional (1D) discontinuous Galerkin morphodynamic model has been devised with application to simulate of dam-break flows over erodible beds with suspended sediment transport. The morphodynamic equations adopt the shallow-water equations (SWE) considering the interaction of sediment transport and bed changes on the flow. A local second-order Runge-Kutta discontinuous Galerkin (RKDG2) model has been reformulated to numerically solve the morphodynamic equations in a fully coupled manner and with a noncapacity sediment model. The model’s implementation is thoroughly detailed with focus on the discretization of the complex source terms, the treatment of wetting and drying, and other stabilizing issues pertaining to high-solution gradients and the transient character of the topography. The model has been favorably applied to replicate experimental dam-break flow over erodible sediment beds.

Validation of 2D shock capturing flood models around a surcharging manhole

Abstract This work offers a detailed validation of finite volume (FV) flood models in the case where horizontal floodplain flow is affected by sewer surcharge flow via a manhole. The FV numerical solution of the 2D shallow water equations is considered based on two approximate Riemann solvers, HLLC and Roe, on both quadrilateral structured and triangular unstructured mesh-types. The models are validated against a high resolution experimental data-set obtained using a physical model of a sewer system linked to a floodplain via a manhole. It was verified that the sensitivity of the models is inversely proportional to the surcharged flow/surface inflow ratio, and therefore requires more calibration from the user especially when concerned with localised modelling of sewer-to-floodplain flow. Our findings provide novel evidence that shock capturing FV-based flood models are applicable to simulate localised sewer-to-floodplain flow interaction.

Closure to “A 2D shallow flow model for practical dam-break simulation”

On p. 312, the authors state that “The classical analytical test of oscillatory flow in a parabolic bowl due to Thacker (1981) has been extended to include friction in 1D by Sampson et al. (2006). Herein, the analytical frictional flow is re-derived and extended to 2D”. The authors then presented equations for a 2D model. In saying that they extended the 1D model to 2D, Wang et al. are claiming that they are the first to derive a 2D model. In fact, the 2D model presented by Wang et al. was originally derived by Sampson et al. (2003). In the 2006 paper by Sampson et al., it is (a) clearly stated that an analytical model had been derived by Sampson et al. in their 2003 paper and (b) in the bibliography, the title of the 2003 paper is given as “Moving boundary shallow water flow in circular paraboloidal basins”, clearly a 2D model. Even if Wang et al. were unable to obtain a copy of the 2003 paper, they did not contact the authors of the paper to get a copy of it. Regardless of whether Wang et al. were able to obtain a copy of the 2003 paper or not, it is clear that Sampson et al. derived the 2D model originally. Sampson et al. assert the right to be regarded as the original authors of the 2D model. I would like an acknowledgment from Wang et al. that Sampson et al. were the original authors of the 2D model that they presented in their paper. I also mention that the minus sign should be removed in the second equation in Eq. (22).