A layer-integrated approach for shallow water free-surface flow computation (original) (raw)
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Development of a generalized multi-layer model for 3-D simulation of free surface flows
International Journal for Numerical Methods in Fluids, 2004
A mathematical model was developed for three-dimensional (3-D) simulation of free surface ows. In this model, the ow depth is divided into a number of layers and shallow water equations are integrated in each layer to derive the hydrodynamic equations. To give a general form to this model, each layer is assumed to be non-horizontal with varying thickness in the ow domain. A non-orthogonal curvilinear coordinate system is employed in the model, to allow for exibility in dealing with the irregular geometry of natural watercourses. Due to the similarity in governing equations, two-dimensional (2-D) depth averaged programs can be developed into a multi-layer model. The development for a depth averaged program and its numerical scheme is described in this paper. Experimental data and semi-analytical solutions are used to evaluate the performance of the model. Three di erent cases of open channel ow are tested: 1-ow in a straight open channel, 2-the ow development region in a channel, and 3-ow in a meandering channel. It is shown that the model has the capability to predict velocity distribution and secondary ows in complex 3-D ow conditions.
A 3D finite element model for free-surface flows
Computers & Fluids, 2009
The present work deals with the validation of 3D finite element model for free-surface flows. The model uses the non-hydrostatic pressure and the eddy viscosities from the conventional linear turbulence model are modified to account for the secondary effects generated by strong channel curvature in the natural rivers with meandering open channels. The unsteady Reynolds-averaged Navier-Stokes equations are solved on the unstructured grid using the Raviart-Thomas finite element for the horizontal velocity components, and the common P1 linear finite element in the vertical direction. To provide the accurate resolution at the bed and the free-surface, the governing equations are solved in the multi-layers system (the vertical plane of the domain is subdivided into fixed thickness layers). The up-to-date k-e turbulence solver is implemented for computing eddy coefficients, the Eulerian-Lagrangian-Galerkin (ELG) temporal scheme is performed for enhancing numerical time integration to guarantee high degree of mass conservation while the CFL restriction is eliminated. The present paper reports on successful validation of the numerical model through available benchmark tests with increasing complexity, using the high quality and high spatial resolution three-dimensional data set collected from experiments.
Lecture Notes in Computer Science, 2005
Validation of 3D finite element model for free-surface flow is conducted using a high quality and high spatial resolution data set. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the complicated channel geometry (e.g. strong channel curvature). A numerical solution is based on the unsteady Reynolds-averaged Navier-Stokes equations without conventional assumption of hydrostatic pressure. The model uses implicit fractional step time stepping, with the characteristic method for convections terms. The eddy viscosity is calculated from the efficient k − turbulence model. The RANS are solved in the multi-layers system (suitable for the vertical stratified fluid flow) to provide the accurate resolution at the bed and free-surface. The model is applied to the 3D curved open channels flows for which experimental data are available for comparison. Good agreement is found between numerical computations and experiments.
Canadian Journal of Civil Engineering, 2008
Velocity gradient between main channel and flood plains in compound channels leads to the formation of a large shear layer and secondary currents between these two subsections. These phenomena in the interaction region bring about a complex three-dimensional nature of the flow in compound channels. To cope with these flows, many numerical investigations have utilized three-dimensional formulations with advanced turbulence models. However, the free surface in many of these models is fixed and rigid-lid assumption has been used. In the present research, three-dimensional shallow water equations were used to calculate the flow field in compound channels. Three-dimensional equations were integrated in layers and were combined with the continuity equation. In this formulation, free-surface elevation was calculated without the need to solve any additional equations. Velocity and bed shear stress distribution and the stage–discharge relationship in compound channels with smooth and rough b...
Shallow Water and Navier-Stokes SPH-like numerical modelling of rapidly varying free-surface flows
2010
Dottorato di Ricerca in Ingegneria Civile (XXII Ciclo) Curriculum: protezione idraulica del territorio, ICAR\02 Renato Vacondio Shallow Water and Navier-Stokes SPH-like numerical modelling of rapidly varying free-surface flows Dissertazione per il conseguimento del titolo di Dottore di Ricerca Tutore: Prof. Paolo Mignosa Co-tutore: Dr. Benedict D. Rogers Coordinatore del Dottorato: Prof. Paolo Mignosa Parma, Gennaio 2010 a Fede
A three-dimensional finite volume model for shallow water flow simulation
Australian journal of basic and applied sciences, 2010
A three-dimensional cell-centred boundary-fitted finite volume model is developed to solve shallow water equations in open channels. An explicit finite volume method is used to discretize the governing equations in a structured and collocated grid system. A special coupling scheme is applied in some cross-section, based on differences of averaged free surface elevation and flow discharge in 3D model and 1D flow data. The proposed scheme can decrease numerical oscillation and increase the accuracy of the model. The model was applied to simulate 3D flow parameters variation in the developing region of a laboratory flume. Computed 3D velocity profiles were drawn and compared in several cross-sections and layers. Comparing the model results with available experimental data confirmed the efficiency of the scheme.
Numerical Simulation of Free Surface Flows
Journal of Computational Physics, 1999
A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar to the volume of fluid (VOF) method, the numerical schemes used to solve the problem are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stokes problem are to be solved. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small rectangular cells, using a forward characteristic method. The generalized Stokes problem is solved using a finite element method on a fixed, unstructured mesh. Numerical results are presented for several test cases: the filling of an S-shaped channel, the filling of a disk with core, the broken dam in a confined domain.
Computers & Fluids, 2010
The main interest of the present study is the simulation of wind-induced currents in closed water bodies with shallow and deep regions. This paper describes a low time consumption numerical modelling technique for the simulation of free-surface flow over a geometrically complex bed. To achieve this, a technique employing coupled two-and three-dimensional flow solvers is developed for simulation of the flow. The conjunctive model consists of an upper part 2D Shallow Water Flow Solver (2D-SWFS) coupled with a 3D pseudo-compressible flow solver (3D-PCFS) for the deep regions with a proper interface boundary condition. The 2D-SWFS and 3D-PCFS solvers are coupled via an interfacial shear stress gradient and pressure effects. Time stepping is performed for the 2D solver, and an iterative procedure is employed by the 3D solver to satisfy the equilibrium constraints for the interfacial boundary. The model is able to consider 2D wetting and drying shallow regions without any underlying deep water. Both the 2D and 3D models use nodal based Galerkin finite volume method (GFVM) for solving the governing equations on the unstructured meshes. The accuracy of both models in solving the effective phenomena is examined by comparing the results of simulated test cases with readily available analytical solutions and experimental measurements. Finally, the accuracy of the conjunctive model is assessed by comparing its results for test cases with analytical solutions and experimental measurements from the literature. The new simulation method is then used to solve a wind-induced flow problem in a basin with deep water surrounded by shallow water parts.
IMPLICIT NUMERICAL SIMULATION OF TWO- AND THREE-DIMENSIONAL FREE-SURFACE FLOW PROBLEMS
The present study proposes a finite-volume implicit numerical scheme for the simulation of two-and three-dimensional free-surface flow problems. The implicit form of the scheme guarantees fast convergence allowing the use of large time steps. The introduction of a non-orthogonal boundary-fitted coordinate system (local coordinates) makes it possible for the model to handle various types of boundary conditions with accuracy. In the case of two-dimensional flow problems, the conservative form of the equations of fluid dynamics is used while the Navier-Stokes equations in combination with the innovative technique of pseudocompressibility are used to describe mathematically the three-dimensional free-surface flow problems. The resulting flow equations are transformed into the local coordinate system and then are solved numerically. The three dimensional scheme is used to analyze the free-surface flow over a double-arc spillway which was mounted in a laboratory flume. Bottom pressures and water levels were measured at various points along the centerline. Successful comparisons between measurements and computed results ensure the credibility of the proposed scheme.
Numerical Modelling and Analysis of Water Free Surface Flows∗
2005
Various environmental engineering applications related to water resources involve unsteady free surface flows. A full 3D models based on Navier-Stokes equations are a good description of the physical features concerning several phenomena as for example lake eutrophication, transport of pollutant, flood in rivers, watershed, etc. However these models are characterized by an important computational effort, that we aim to reduce in some case by the help of 2D models or by appropriate coupling models of different dimensions and by the use of the parallel algorithmic trough HPCN facilities. In this work, we present an overview of some approximations methodologies and techniques for an efficient numerical modelling of water free surface problems in a finite element context.