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

• Published in: Journal of hydrodynamics. Series B 2011-04, Vol.23 (2), p.212-223
• Main Authors: HU, De-chao, FAN, Bei-lin, WANG, Guang-qian, ZHANG, Hong-wu
• Format: Article
• Language: English
• Subjects: 3-D; Computational fluid dynamics; Computer simulation; Engineering; Engineering Fluid Dynamics; Fluid flow; Hydrology/Water Resources; Linear systems; Mathematical models; non-hydrostatic; Numerical and Computational Physics; numerical model; Poisson equation; pressure-splitting; semi-implicit; sigma; sigma-coordinate; Simulation; Turbulence; Turbulent flow; 三维数值模型; 共轭梯度法; 半隐式; 坐标变换; 自由表面流; 静水压力; 非对称线性系统
• ISSN: 1001-6058; 1878-0342
• DOI: 10.1016/S1001-6058(10)60106-0

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.