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.     

Towards a hydrodynamic modelling framework appropriate for applications in urban flood assessment and mitigation using heterogeneous computing

We present a new hydrodynamic modelling framework capable of fully exploiting modern graphics and central processing units (GPUs and CPUs) from any of the mainstream vendors, to be used in the design and assessment of sustainable drainage systems. A finite-volume Godunov-type scheme is combined with the HLLC Riemann solver to create a robust numerical model which correctly addresses wetting and drying and transient flow conditions, and is suitable for application to a wide range of flood simulations. The software is tested with a three day flood event in Carlisle during 2005, at resolutions from 25 m to 2 m. Run-times are significantly reduced without compromising numerical accuracy. Excellent agreement is found between the simulation results and a comprehensive post-event survey. Changes in sensitivity to Manning's n are examined at different resolutions, with changes to the floodplain found to have little influence at 2 m resolution.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL DAM-BREAK FLOWS IN CURVED CHANNELS

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

A second-order Finite Volume Method for pipe flow with water column separation

A second-order explicit Finite Volume Method (FVM) based on Godunov-type schemes is presented and applied to water column separation (WCS) in pipelines. The treatment of two-phase fluid in the model is similar to the ideas of the classic discrete vapor cavity model (DVCM) based on method of characteristics (MOC). The challenge in using the FVM is how to capture vapor cavities and predict their growth and collapse. The FVM introduced here assumes the vaporous cavity is concentrated at the middle of control volume, and divides the local control volume into two equal halves, in order to calculate the vapor cavity volume. The proposed model is based on the exact Reimann solution of the coupled continuity and momentum equations, and second-order accuracy is achieved by means of data reconstruction based on slope limiter, an approach which prevents the development of spurious oscillations near in the vicinity of high gradients. Predictions of FVM-DVCM for transient pressures caused by WCS and rejoining are compared to published experimental data and to numerical results from the classic DVCM. Pressure results from FVM-DVCM show considerably better agreement with experimental data and significantly avoid unrealistic artificial spikiness with finer grids.     

二维溃坝波遇障碍物的水流泥沙数值模拟

本文通过对浅水方程进行Godunov差分离散和对泥沙运动方程进行一阶迎风差分离散，建立了平面l二维溃坝水流泥沙数值模型。在算例中计算了溃坝波遇障碍物后的水流反射、绕射及泥沙冲淤，计算结果表明，溃坝波遇障碍物后会产生明显的反射和绕射，并在障碍物前形成壅水、障碍物的侧面会发生剧烈的冲刷，障碍物前后则会发生局部淤积。本模型能够较好地模拟溃坝间断水流的运动，结果符合水流泥沙运动的基本规律。     

NUMERICAL SIMULATION FOR 2D SHALLOW WATER EQUATIONS BY USING GODUNOV-TYPE SCHEME WITH UNSTRUCTURED MESH

1. INTRODUCTION In general, the geometry of natural water areas, such as rivers, coasts and lakes, is irregular, so that the application of mathematical models with structured mesh is quite limited and the accuracy could not be ensured especially as the m…     

A COUPLED MORPHODYNAMIC MODEL FOR APPLICATIONS INVOLVING WETTING AND DRYING

This work presents a new finite volume Godunov-type model for predicting morphological changes under the rapidly varying flood conditions with wetting and drying.The model solves the coupled shallow water and Exner equations,with the interface fluxes evaluated by an Harten-Lax-van Leer-Contact(HLLC) approximate Riemann solver.Well-balanced solution is achieved using the surface gradient method and wetting and drying are handled by a non-negative reconstruction approach.The new model is validated against several theoretical benchmark tests and promising results are obtained.     

An efficient dynamic uniform Cartesian grid system for inundation modeling

A dynamic uniform Cartesian grid system was developed in order to reduce the computational time in inundation simulation using a Godunov-type finite volume scheme. The reduction is achieved by excluding redundant dry cells, which cannot be effectively avoided with a conventional Cartesian uniform grid system, as the wet area is unknown before computation. The new grid system expands dynamically with wetting, through addition of new cells according to moving wet-dry fronts. The new grid system is straightforward in implementation. Its application in a field-scale flood simulation shows that the new grid system is able to produce the same results as the conventional grid, but the computational efficiency is fairly improved.     

NUMERICAL SIMULATION FOR SHALLOW FLOW AND POLLUTANT DISPERSION BASED ON QUAD-TREE MESHES

1. INTRDUCTION Natural flow domains have complicated boundary configurations, which may themselves strongly influence the interior flow patterns.Sometimes, high-gradient zones and local areas which are relatively important in some problems are included in…     

A high-order one-step sub-cell force-based discretization for cell-centered Lagrangian hydrodynamics on polygonal grids

We present a one-step high-order cell-centered numerical scheme for solving Lagrangian hydrodynamics equations on unstructured grids. The underlying finite volume discretization is constructed through the use of the sub-cell force concept invoking conservation and thermodynamic consistency. The high-order extension is performed using a one-step discretization, wherein the fluxes are computed by means of a Taylor expansion. The time derivatives of the fluxes are obtained through the use of a node-centered solver which can be viewed as a two-dimensional extension of the Generalized Riemann Problem methodology introduced by Ben-Artzi and Falcovitz.