High-Resolution Numerical Simulations For Complex Water Flow

In this paper,free surface complex flow problems,using shallow water equations of source terms and Navier-Stokes equations modeling.a high-order and high-resolution discrete model for shallow water equation based on unstructured grid finite volume technique and a hydrodynamic pressure discrete model for Navier-Stokes equation base on structured layered grid semi-implicit finite difference numerical technique are established for the free-surface practical flow problems.For one-dimensional shallow water equations(Saint-Venant equations),in based on a space staggered grid system,a semi-implicit discrete scheme that has strong capacity to capture discontinuous is applied,simultaneity,the flux limiter method, is implemented to control the momentum conservative of the proposed scheme.For bed slope source term and friction slope source terms in two-dimensional shallow water,we present a fully implicit method consists of treating the bed slope source term as the divergence of a proper matrix.This method guarantees harmoniousness and stability of model.Based on Eulerian-Lagrangian method and k-εequations turbulence model,a semi-implicit discrete model used the structured grid for three-dimensional Navier-Stokes equations with stability hydrodynamic pressure is established.Applying object oriented programming language C# based on Visual studio.net2005 compiling environment,the writing,debugging and verification of the program is done:First,based on space staggered grid system,using semi-implicit scheme Saint-Venant equations discretized.In order to improve the accuracy,the flux limiter method has been used. This high-order resolution method switches between the second-order approximation when the data are sufficiently smooth and the first-order approximation near a discontinuity.This treatment avoids nonphysical numerical oscillations near a discontinuity.A few computational examples on classical test cases are given to illustrate the properties of the present method in terms of balance,accuracy and efficiency.Second,using technique of unstructured triangle grid,a high-order and high-resolution finite volume numerical discreted model is established for the 2D shallow water equations. The proposed method consists of writing the bed slope source term as the divergence of a proper matrix,related to the static force due to bottom slope,The friction terms are treated fully implicitly to prevent numerical instabilities.The interface between dry and wet region in this model is using a moving boundary that is satisfied mass conservation.This technique improves the ability of treating the moving boundary in unsteady flow problem.The technique of space reconstruction and method of flux limiter are employed to achieve high-order spatial accuracy and to prevent nonphysical oscillations.Simultaneous,using eigen decomposition method for boundary condition is processed,computed flux of boundary edge, furthermore,the flux substitutes into solution of the finite volume discreted equations. Numerical tests of two-dimensional oblique hydraulic jump,dam break and Xin Anjiang model are employed to test the this two-dimensional model's accuracy,conservation and capability of handling discontinuous solutions.To apply the model in practical flows,an example of a dam break flood of Ying Nahe reservoir is applied to prove the model's harmoniousness and capability of simulating practical flows.Third,based on horizontal structured grid and vertical directly layered grid treatment technology,a three-dimensional Navier-Stokes equations of free-surface flow model is established in a hydrodynamic pressure semi-implicit finite difference numerical discrete scheme.In water depth direction,free-surface equation can be obtained by integral continuity equation,which is satisfied kinematic condition at the free surface.To solve this equation and momentum equation,the free surface can be captured directly.The hydrodynamic pressure correction is solved from the pressure Poisson equation(PPE).At outflow,a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection.For the sponge layer,the artificial damping terms are added to the right-hand side of horizontal momentum equation,at the end of the sponge layer,the radiation condition is used further to enhance wave absorption.In order to make three-dimensional model closed, turbulence model uses k-εequations to solve eddy viscosity coefficient.By three-dimensional linear standing wave,the wave propagation over a bar of scheldt flume experiment carried at Delft hydraulics and tidal current field simulation of waters of between Denmark and Sweden etc example,the model is verified to have advantages such as stability, high efficiency etc,and proved suitable for the simulation both water body of large range and long period.Numerical models established by this paper provide good results by comparing numerical results with analytical solution or experimental data.