Implementation of an Approximate Conformal UPML in 2-D DGTD

Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the k-ε turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a 180° curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.

Low Speed Preconditioning Algorithm Used in the Process of Calculating Euler Equation

This paper describes a numerical method for solving the unsteady Euler equation at any speed. In the process of calculating Euler's equation, the control equation in orthogonal curvilinear coordinate system is discretized by the finite -volume scheme based on the center-difference method, and convection flux used Jameson central deference scheme was solved at every pseudo time step, and the Runge-Kutta method, dual-time algorithm and the implicit LU-SGS add preconditioning algorithm are used for time-marching. For obtaining the numerical solution of two-dimensional unsteady flow around a cylinder and the flow of the Convex Hull, finding that the calculated results agree well with literature values and theoretical analytical solution.

Extension of Material Derivative Concept in Fluid Mechanics

The original definition of material derivative is changing rate relative to the time of a physical quantity which belongs to a fluid particle. But when studying fluid mechanics problems, need in certain cases to calculate the material derivative of some quantities which don’t belong to a fluid particle, such as calculating the material derivative of base vectors of orthogonal curvilinear coordinate system. The original definition of material derivative isn’t suitable for these quantities. Calculating material derivative of these quantities is not clear in concept. To solve this problem, thorough analysis about material derivative was made according to the original definition and calculation formula of material derivative. Results found that the concept of material derivative can be extended and so can apply to any quantities which don’t belong to a fluid particle and are defined in flow fields, including vector or scalar, physical quantities or non physical quantities.

STUDY ON INFLUENCE OF BAIMAO SANDBANK CONTROL PROJECT IN SOUTHERN BRANCH OF THE YANGTZE RIVER ESTUARY, CHINA

The author establishes the Yangtze estuary 2D tidal and sediment mathematical model based on the orthogonal curvilinear coordinate system. The erosion and siltation of engineering section under the hydrological conditions of flood season, dry season and the great flood after the Baimao Sand control engineering is calculated. Preliminarily expounds the correlation of Baimao Sand and Biandan Sand and the impact of Biandan Sand after the Baimao Sand control engineering is implemented.

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.