715 research outputs found

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

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    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

    Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics

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    This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties

    Depth-averaged and 3D Finite Volume numerical models for viscous fluids, with application to the simulation of lava flows

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    This Ph.D. project was initially born from the motivation to contribute to the depth-averaged and 3D modeling of lava flows. Still, we can frame the work done in a broader and more generalist vision. We developed two models that may be used for generic viscous fluids, and we applied efficient numerical schemes for both cases, as explained in the following. The new solvers simulate free-surface viscous fluids whose temperature changes are due to radiative, convective, and conductive heat exchanges. A temperature-dependent viscoplastic model is used for the final application to lava flows. Both the models behind the solvers were derived from mass, momentum, and energy conservation laws. Still, one was obtained by following the depth-averaged model approach and the other by the 3D model approach. The numerical schemes adopted in both our models belong to the family of finite volume methods, based on the integral form of the conservation laws. This choice of methods family is fundamental because it allows the creation and propagation of discontinuities in the solutions and enforces the conservation properties of the equations. We propose a depth-averaged model for a viscous fluid in an incompressible and laminar regime with an additional transport equation for a scalar quantity varying horizontally and a variable density that depends on such transported quantity. Viscosity and non-constant vertical profiles for the velocity and the transported quantity are assumed, overtaking the classic shallow-water formulation. The classic formulation bases on several assumptions, such as the fact that the vertical pressure distribution is hydrostatic, that the vertical component of the velocity can be neglected, and that the horizontal velocity field can be considered constant with depth because the classic formulation accounts for non-viscous fluids. When the vertical shear is essential, the last assumption is too restrictive, so it must relax, producing a modified momentum equation in which a coefficient, known as the Boussinesq factor, appears in the advective term. The spatial discretization method we employed is a modified version of the central-upwind scheme introduced by Kurganov and Petrova in 2007 for the classical shallow water equations. This method is based on a semi-discretization of the computational domain, is stable, and, being a high-order method, has a low numerical diffusion. For the temporal discretization, we used an implicit-explicit Runge-Kutta technique discussed by Russo in 2005 that permits an implicit treatment of the stiff terms. The whole scheme is proved to preserve the positivity of flow thickness and the stationary steady-states. Several numerical experiments validate the proposed method, show the incidence on the numerical solutions of shape coefficients introduced in the model and present the effects of the viscosity-related parameters on the final emplacement of a lava flow. Our 3D model describes the dynamics of two incompressible, viscous, and immiscible fluids, possibly belonging to different phases. Being interested in the final application of lava flows, we also have an equation for energy that models the thermal exchanges between the fluid and the environment. We implemented this model in OpenFOAM, which employs a segregated strategy and the Finite Volume Methods to solve the equations. The Volume of Fluid (VoF) technique introduced by Hirt and Nichols in 1981 is used to deal with the multiphase dynamics (based on the Interphase Capturing strategy), and hence a new transport equation for the volume fraction of one phase is added. The challenging effort of maintaining an accurate description of the interphase between fluids is solved by using the Multidimensional Universal Limiter for Explicit Solution (MULES) method (described by Marquez Damian in 2013) that implements the Flux-Corrected Transport (FCT) technique introduced by Boris and Book in 1973, proposing a mix of high and low order schemes. The choice of the framework to use for any new numerical code is crucial. Our contribution consists of creating a new solver called interThermalRadConvFoam in the OpenFOAM framework by modifying the already existing solver interFoam (described by Deshpande et al. in 2012). Finally, we compared the results of our simulations with some benchmarks to evaluate the performances of our model

    Three-dimensional numerical analysis of flow structure and sediment transport process in open channels

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    This research project focuses on the analysis and prediction of flow structures and sediment transport process in open channels by using three-dimensional numerical models. The numerical study was performed using the open source computational fluid dynamics (CFD) solver based on the finite volume method (FVM) – OpenFOAM. Turbulence is treated by means of the two main methodologies; i.e. Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS). The free surface is tracked using the Volume of Fluid method (VOF). In addition, a new multi-dimensional model for sediment transport based on the Eulerian two-phase mathematical formulation is applied. The results obtained from the different numerical configurations are verified and validated against experimental data sets published in important research journals. The main characteristics of the flow structures are studied by using three set-up cases in steady and unsteady-state (transient) hydraulic flow conditions. On the other hand, the new multi-dimensional model for sediment transport is applied to predict the local scour caused by submerged wall jet test-case. Non-uniform structured elements are used in the grid configuration of the computational domains. A mesh sensitivity analysis is performed in each test-case study in order to obtain independent grid results. This analysis provides a balance between accuracy and optimal computational time. The results demonstrate that the three-dimensional numerical configurations satisfactorily reproduce the temporal variation of the different variables under study with correct trends and high correlation with the experimental values. Regarding the analysis and prediction of the flow structures, the results show the importance of the turbulence approach in the numerical configuration. On the other hand, the results of the new multi-dimensional two-phase model allow to analyze the full dynamics for sediment transport (concentration profile). Although the numerical results are satisfactory, the application of three-dimensional numerical models in field-scale cases requires a high computational resource.Este trabajo de investigación se enfoca en el análisis y predicción de las estructuras de flujo y el proceso de transporte de sedimentos en canales abiertos mediante el uso de modelos numéricos tridimensionales. El estudio numérico se realizó utilizando el software de dinámica de fluidos computacional o CFD (por sus siglas en inglés) basado en el método de volúmenes finitos (FVM) - OpenFOAM. La influencia de la turbulencia es analizada con las dos principales metodologías, LES (Large Eddy Simulation) y RANS (Reynolds-Averaged Navier¿ Stokes); mientras que el método VOF (Volume of Fluid) es usado para la captura de la superficie libre del agua. Además, se aplica un nuevo modelo multidimensional para el transporte de sedimentos basado en la formulación matemática Euleriana de dos fases. Los resultados obtenidos de las diferentes configuraciones numéricas son verificados y validados con datos experimentales publicados en importantes revistas de investigación. Las características principales de las diferentes estructuras de flujo se estudian en tres casos que incluyen condiciones de flujo estacionario y no estacionario (también conocido como flujo transitorio). Por otro lado, el nuevo modelo multidimensional para el estudio de transporte de sedimentos se aplica para predecir la socavación producida en un caso experimental de chorro de fondo sobre lecho erosionable. Los dominios computacionales son configurados con elementos estructurados no uniformes. Además, se realiza un análisis de sensibilidad en cada caso de estudio con el objetivo de obtener resultados independientes del tamaño de mallas utilizadas. Este análisis permite encontrar un equilibrio entre la precisión de los resultados y un tiempo de cálculo óptimo. Los resultados muestran que las configuraciones numéricas son capaces de reproducir satisfactoriamente las diferentes variables en estudio, con tendencias correctas y una alta correlación con los valores experimentales. Con respecto al análisis y predicción de las estructuras de flujo, los resultados revelan la importancia que tiene el uso del modelo de turbulencia en la configuración numérica. Por otro lado, los resultados obtenidos con el uso de un nuevo modelo multidimensional de dos fases permiten analizar la dinámica completa del transporte de sedimentos (perfil de concentración). Aunque los resultados numéricos son satisfactorios, la aplicación de modelos tridimensionales en casos a escala de campo exige un considerable recurso computacional en velocidad de cálculo y almacenamiento de datos

    Three-dimensional numerical analysis of flow structure and sediment transport process in open channels

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    This research project focuses on the analysis and prediction of flow structures and sediment transport process in open channels by using three-dimensional numerical models. The numerical study was performed using the open source computational fluid dynamics (CFD) solver based on the finite volume method (FVM) – OpenFOAM. Turbulence is treated by means of the two main methodologies; i.e. Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS). The free surface is tracked using the Volume of Fluid method (VOF). In addition, a new multi-dimensional model for sediment transport based on the Eulerian two-phase mathematical formulation is applied. The results obtained from the different numerical configurations are verified and validated against experimental data sets published in important research journals. The main characteristics of the flow structures are studied by using three set-up cases in steady and unsteady-state (transient) hydraulic flow conditions. On the other hand, the new multi-dimensional model for sediment transport is applied to predict the local scour caused by submerged wall jet test-case. Non-uniform structured elements are used in the grid configuration of the computational domains. A mesh sensitivity analysis is performed in each test-case study in order to obtain independent grid results. This analysis provides a balance between accuracy and optimal computational time. The results demonstrate that the three-dimensional numerical configurations satisfactorily reproduce the temporal variation of the different variables under study with correct trends and high correlation with the experimental values. Regarding the analysis and prediction of the flow structures, the results show the importance of the turbulence approach in the numerical configuration. On the other hand, the results of the new multi-dimensional two-phase model allow to analyze the full dynamics for sediment transport (concentration profile). Although the numerical results are satisfactory, the application of three-dimensional numerical models in field-scale cases requires a high computational resource.Este trabajo de investigación se enfoca en el análisis y predicción de las estructuras de flujo y el proceso de transporte de sedimentos en canales abiertos mediante el uso de modelos numéricos tridimensionales. El estudio numérico se realizó utilizando el software de dinámica de fluidos computacional o CFD (por sus siglas en inglés) basado en el método de volúmenes finitos (FVM) - OpenFOAM. La influencia de la turbulencia es analizada con las dos principales metodologías, LES (Large Eddy Simulation) y RANS (Reynolds-Averaged Navier¿ Stokes); mientras que el método VOF (Volume of Fluid) es usado para la captura de la superficie libre del agua. Además, se aplica un nuevo modelo multidimensional para el transporte de sedimentos basado en la formulación matemática Euleriana de dos fases. Los resultados obtenidos de las diferentes configuraciones numéricas son verificados y validados con datos experimentales publicados en importantes revistas de investigación. Las características principales de las diferentes estructuras de flujo se estudian en tres casos que incluyen condiciones de flujo estacionario y no estacionario (también conocido como flujo transitorio). Por otro lado, el nuevo modelo multidimensional para el estudio de transporte de sedimentos se aplica para predecir la socavación producida en un caso experimental de chorro de fondo sobre lecho erosionable. Los dominios computacionales son configurados con elementos estructurados no uniformes. Además, se realiza un análisis de sensibilidad en cada caso de estudio con el objetivo de obtener resultados independientes del tamaño de mallas utilizadas. Este análisis permite encontrar un equilibrio entre la precisión de los resultados y un tiempo de cálculo óptimo. Los resultados muestran que las configuraciones numéricas son capaces de reproducir satisfactoriamente las diferentes variables en estudio, con tendencias correctas y una alta correlación con los valores experimentales. Con respecto al análisis y predicción de las estructuras de flujo, los resultados revelan la importancia que tiene el uso del modelo de turbulencia en la configuración numérica. Por otro lado, los resultados obtenidos con el uso de un nuevo modelo multidimensional de dos fases permiten analizar la dinámica completa del transporte de sedimentos (perfil de concentración). Aunque los resultados numéricos son satisfactorios, la aplicación de modelos tridimensionales en casos a escala de campo exige un considerable recurso computacional en velocidad de cálculo y almacenamiento de datos.Postprint (published version

    A new family of semi-implicit Finite Volume / Virtual Element methods for incompressible flows on unstructured meshes

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    We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between explicit and implicit terms that may arise either from the multi-scale nature of the governing equations, which involve both slow and fast scales, or in the context of projection methods, where the numerical solution is projected onto the physically meaningful solution manifold. We propose to use a high order finite volume (FV) scheme for the explicit terms, ensuring conservation property and robustness across shock waves, while the virtual element method (VEM) is employed to deal with the discretization of the implicit terms, which typically requires an elliptic problem to be solved. The numerical solution is then transferred via suitable L2 projection operators from the FV to the VEM solution space and vice-versa. High order time accuracy is achieved using the semi-implicit IMEX Runge-Kutta schemes, and the novel schemes are proven to be asymptotic preserving and well-balanced. As representative models, we choose the shallow water equations (SWE), thus handling multiple time scales characterized by a different Froude number, and the incompressible Navier-Stokes equations (INS), which are solved at the aid of a projection method to satisfy the solenoidal constraint of the velocity field. Furthermore, an implicit discretization for the viscous terms is devised for the INS model, which is based on the VEM technique. Consequently, the CFL-type stability condition on the maximum admissible time step is based only on the fluid velocity and not on the celerity nor on the viscous eigenvalues. A large suite of test cases demonstrates the accuracy and the capabilities of the new family of schemes to solve relevant benchmarks in the field of incompressible fluids

    Numerical Simulation of a Dam Break Flow Using Finite Difference Approach

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    Each and every phenomenon that occurs in this world is governed by some mathematical equations or functions, that means every incident can be represented in terms of mathematical functions of some independent variables. Likewise the flow that occurs after the break of a dam is represented by a set of some non-linear hyperbolic mathematical equations known as shallow water equations those are obtained from the profundity incorporating the Navier-Stokes equations where the horizontal dimensions are greater than the vertical dimensions. Investigation of dam break stream numerically is a fundamental piece of water driven designing practice. Estimation of peak flood profundity, its time of occurrence at a predefined area, wave fronts and evaluation of its fetch can be possible better through numerical models than that of physically-based models. In this present research work this system of shallow water equations are discretised by finite difference method (mainly using Mac Cormack method) for preparing the codes for programming in both MATLAB and FORTRAN to prepare a numerical model with all the required boundary conditions that used happen during a dam break. The numerical method used here for analysing the above governing mathematical statements are upgraded by utilizing the technique for fragmentary strides for rearranging application, treating the grinding slant, a hardened source term, point-certainly, for numerical swaying control and security. This prepared model is again validated with some documented results to know the accuracy and stability of the numerical discritisation and compared with a practical dam break case study analysed with HEC-RAS software so as to compare the different aspects of the model and the software. The present numerical examination has the capacity for resolution stuns, complex bed geometry including the impact of bed inclines and unpleasantness. So the above scheme is much effective in analysing the set of SWES than the former one

    A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers

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    We present a novel staggered semi-implicit hybrid FV/FE method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time of the conservative Saint-Venant equations with bottom friction terms leads to its decomposition into a first order hyperbolic subsystem containing the nonlinear convective term and a second order wave equation for the pressure. For the spatial discretization of the free surface elevation an unstructured mesh of triangular simplex elements is considered, whereas a dual grid of the edge-type is employed for the computation of the depth-averaged momentum vector. The first stage of the proposed algorithm consists in the solution of the nonlinear convective subsystem using an explicit Godunov-type FV method on the staggered grid. Next, a classical continuous FE scheme provides the free surface elevation at the vertex of the primal mesh. The semi-implicit strategy followed circumvents the contribution of the surface wave celerity to the CFL-type time step restriction making the proposed algorithm well-suited for low Froude number flows. The conservative formulation of the governing equations also allows the discretization of high Froude number flows with shock waves. As such, the new hybrid FV/FE scheme is able to deal simultaneously with both, subcritical as well as supercritical flows. Besides, the algorithm is well balanced by construction. The accuracy of the overall methodology is studied numerically and the C-property is proven theoretically and validated via numerical experiments. The solution of several Riemann problems attests the robustness of the new method to deal also with flows containing bores and discontinuities. Finally, a 3D dam break problem over a dry bottom is studied and our numerical results are successfully compared with numerical reference solutions and experimental data
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