Numerical Simulation of Pollutant Transport in a Shallow-Water System on the Cell Heterogeneous Processor

[Abstract] This paper presents an implementation, optimized for the Cell processor, of a finite volume numerical scheme for 2D shallow-water systems with pollutant transport. A description of the special architecture and programming required by the Cell processor motivates the methodology to develop optimized implementations for this platform. This process involves parallelization, data structure reorganization, explicit transfers of data and computation vectorization. Our implementation, tested using a realistic problem, achieves very good speedups with respect to the sequential execution on a standard CPU.This work was partially supported by the Science and Innovation Ministry of Spain (Projects TIN2010-16735, MTM2010-21135-C02-01 and MTM2009-11923), Xunta de Galicia CN2012/211 (partially supported by FEDER funds), and the FPU program of the Spanish Government (ref AP2009-4752)Xunta de Galicia; CN 2012/21

An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The scheme is incorporated into a two-dimensional (2D) cell-centered Godunov-type finite volume model as proposed in Hou et al. (2013a,c) to solve the shallow water equations (SWEs). The MUSCL scheme renders the model to preserve the well-balanced property and achieve high accuracy and efficiency for shallow flow simulations over uneven terrains. Furthermore, the scheme is directly applicable to all triangular grids. Application to several numerical experiments verifies the efficiency and robustness of the current new MUSCL scheme

An unstructured finite-volume method for coupled models of suspended sediment and bed load transport in shallow-water flows

The aim of this work is to develop a well-balanced finite-volume method for the accurate numerical solution of the equations governing suspended sediment and bed load transport in two-dimensional shallow-water flows. The modelling system consists of three coupled model components: (i) the shallow-water equations for the hydrodynamical model; (ii) a transport equation for the dispersion of suspended sediments; and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite-volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. In this paper, we also employ an adaptive procedure in the finite-volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes and incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases, which demonstrate the accuracy and robustness of the method and its applicability in predicting dam-break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon

Solution of fully-coupled shallow water equations and contaminant transport using a primitive variable Riemann solver and a semi-discrete SUPG method

In the present dissertation, a finite volume and a finite element model are developed and tuned for the solution of the fully-coupled two-dimensional Shallow Water and Contaminant transport Equations with arbitrary bed topography and wetting-drying fronts. A Riemann-solver finite volume scheme, using primitive variables rather than conserved variables, and a semi-discrete Streamline Upwind Petrov-Galerkin (SUPG) method in finite element context are applied to compare the performance of these two numerical models. The Riemann-solver scheme is based on the unstructured finite volume discretization using primitive-variable Roe-flux approximation with an entropy fix. Second-order accuracy in space and time, an implicit scheme based on Newton-iterative algorithm, and an Euler explicit scheme are applied for the finite volume model. For the SUPG finite element model, a new exact source-term balancing method is introduced in this study. This new balancing method satisfies the C-property for both still water and dry regions on a non-flat bed. Two different stabilization terms are applied to compare their performance for wet-bed problems and a shock-capturing scheme is implemented to accommodate shock wave fronts. Linear triangular elements are used to decompose the computational domain and a second-order backward differentiation (BDF2) implicit method is used for the time integration. The resulting nonlinear system is solved using a Newton-type method where the linear system is solved at each step using the Generalized Minimal Residual (GMRES) algorithm. Both finite volume and finite element formulations are applied to moving-boundary problems on fixed numerical meshes. In order to examine the accuracy and robustness of the present scheme to predict the flow variables and contaminant transport, numerical results are verified by several test cases. These cases include wet and dry dam break problems, evolution of a dam break wave with an obstacle downstream of the dam, oscillation of a bead of water in a parabolically-shaped basin, supercritical flow in a constricted channel, as well as advection and diffusion of contaminant with the flow. The scenario of contaminant transport in a notional river is also simulated to demonstrate that the present work can be implemented on practical applications involving flooding and contaminant transport

A New Two Dimensional Model for Pollutant Transport in Ajichai River

Accurate prediction of pollution control and environmental protection need a good understanding of pollutant dynamics. Numerical model techniques are important apparatus in this research area. So a 2500 line FORTRAN 95 version code was conducted in which using approximate Riemann solver, couples the shallow water and pollution transport agents in two dimensions by the aid of unstructured meshes. A multidimensional linear reconstruction technique and multidimensional slope limiter were implemented to achieve a second-order spatial accuracy. The courant number ruled as a control parameter for stability conditions and a third order Runge-Kutta method was performed for equation discretizations. For Code verifications another author's case study was examined. The numerical results show that the model could accurately predict the flow dynamics and pollutant transport in Ajichai River

Implicit finite volume simulation of 2D shallow water flows in flexible meshes

In this work, an implicit method for solving 2D hyperbolic systems of equations is presented, focusing on the application to the 2D shallow water equations. It is based on the first order Roe''s scheme, in the framework of finite volume methods. A conservative linearization is done for the flux terms, leading to a non-structured matrix for unstructured meshes thus requiring iterative methods for solving the system. The validation is done by comparing numerical and exact solutions in both unsteady and steady cases. In order to test the applicability of the implicit scheme to real world situations, a laboratory scale tsunami simulation is carried out and compared to the experimental data. The implicit schemes have the advantage of the unconditional stability, but a quality loss in the transient solution can appear for high CFL numbers. The properties of the scheme are well suited for the simulation of unsteady shallow water flows over irregular topography using all kind of meshes