A SEMI-IMPLICIT 3-D NUMERICAL MODEL USING SIGAM-COORDINATE FOR NON-HYDROSTATIC PRESSURE FREE-SURFACE FLOWS  

作　　者：HU De-chao FAN Bei-lin WANG Guang-qian ZHANG Hong-wu 

机构地区：[1]State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China [2]Yangtze River Scientific Research Institute, Wuhan 430010, China

出　　处：《Journal of Hydrodynamics》2011年第2期212-223,共12页水动力学研究与进展B辑（英文版）

基　　金：Project supported by the National Key Basic Research Program of China (973 Program, Grant No. 2007CB714100);the Key Project of National Natural Science Foundation of China (Grant No. 51039003);supported by the Yangtze River Scientific Research Institute project (Grant No. CKSQ2010075)

摘　　要：A 3-D numerical formulation is proposed on the horizontal Cartesian, vertical sigma-coordinate grid for modeling non-hydrostatic pressure flee-surface flows. The pressure decomposition technique and 0 semi-implicit method are used, with the solution procedure being split into two steps. First, with the implicit parts of non-hydrostatic pressures excluded, the provisional velocity field and free surface are obtained by solving a 2-D Poisson equation. Second, the theory of the differential operator is employed to derive the 3-D Poisson equation for non-hydrostatic pressures, which is solved to obtain the non-hydrostatic pressures and to update the provisional velocity field. When the non-orthogonal sigma-coordinate transformation is introduced, additional terms come into being, resulting in a 15-diagonal, diagonally dominant but unsymmetric linear system in the 3-D Poisson equation for non-hydrostatic pressures. The Biconjugate Gradient Stabilized （BiCGstab） method is used to solve the resulting 3-D unsymmetric linear system instead of the conjugate gradient method, which can only be used for symmetric, positive-definite linear systems. Three test cases are used for validations. The successful simulations of the small-amplitude wave, a supercritical flow over a ramp and a turbulent flow in the open channel indicate that the new model can simulate well non-hydrostatic flows, supercritical flows and turbulent flows.A 3-D numerical formulation is proposed on the horizontal Cartesian, vertical sigma-coordinate grid for modeling non-hydrostatic pressure flee-surface flows. The pressure decomposition technique and 0 semi-implicit method are used, with the solution procedure being split into two steps. First, with the implicit parts of non-hydrostatic pressures excluded, the provisional velocity field and free surface are obtained by solving a 2-D Poisson equation. Second, the theory of the differential operator is employed to derive the 3-D Poisson equation for non-hydrostatic pressures, which is solved to obtain the non-hydrostatic pressures and to update the provisional velocity field. When the non-orthogonal sigma-coordinate transformation is introduced, additional terms come into being, resulting in a 15-diagonal, diagonally dominant but unsymmetric linear system in the 3-D Poisson equation for non-hydrostatic pressures. The Biconjugate Gradient Stabilized （BiCGstab） method is used to solve the resulting 3-D unsymmetric linear system instead of the conjugate gradient method, which can only be used for symmetric, positive-definite linear systems. Three test cases are used for validations. The successful simulations of the small-amplitude wave, a supercritical flow over a ramp and a turbulent flow in the open channel indicate that the new model can simulate well non-hydrostatic flows, supercritical flows and turbulent flows.

关 键 词：3-D numerical model NON-HYDROSTATIC sigma-coordinate SEMI-IMPLICIT pressure-splitting 

分 类 号：O241.82[理学—计算数学] TV863[理学—数学]