Jaan Hui Pu

Source term treatment of SWEs using surface gradient upwind method

Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Evaluations of SWEs and SPH Numerical Modelling Techniques for Dam Break Flows

Abstract The standard shallow water equations (SWEs) model is often considered to provide weak solutions to the dam-break flows due to its depth-averaged shock-capturing scheme assumptions. In this study, an improved SWEs model using a recently proposed Surface Gradient Upwind Method (SGUM) is used to compute dam-break flows in the presence of a triangular hump. The SGUM allows the SWEs model to stably and accurately reproduce the highly complex shock currents caused by the dam-break event, as it improves the treatment of SWEs numerical source terms, which is particularly crucial for simulating the wet/dry front interface of the dam-break flow. Besides, an Incompressible Smoothed Particle Hydrodynamics (ISPH) modeling technique is also employed in this study to compare with the performance of the SGUM-SWEs model. The SPH method is totally mesh free and thus it can efficiently track the large free surface deformation. The ISPH approach uses a strictly incompressible two-step semi-implicit solution method. By reproducing a documented experimental dam-break flow, it has demonstrated that both model simulation results gave good agreement with the experimental data at different measurement locations. However, the ISPH simulations showed a better prediction of the dam-break peak wave building-up time, where its superiority was demonstrated. Furthermore, the ISPH model could also predict more detailed flow surface profiles across the streamwise flow direction and the velocity and pressure structures.

Velocity Distribution in Open Channel Flows: Analytical Approach for the Outer Region

AbstractThis paper presents an integration procedure for the Reynolds-averaged Navier-Stokes equations for the determination of the distribution of the streamwise velocity using the vertical component. This procedure is dedicated to the outer region and central part of channels. The proposed model is applicable to both rough and smooth flow regimes, provided the velocity at the inner-outer boundary has been properly defined. To generate a simplified expansion, a number of hypotheses are proposed, focusing in particular on the analytical modeling of the vertical component by adopting a negligible viscosity. The proposed hypotheses are validated by the experimental data existing in the literature. The proposed simplified expansion is studied through a sensitivity analysis and proved consistent in regards to model experimental data. The proposed model seems capable of demonstrating different kinds of flows, including dip phenomenon flow patterns.

Shallow sediment transport flow computation using time-varying sediment adaptation length

Abstract Based on the common approach, the adaptation length in sediment transport is normally estimated astemporally independent. However, this approach might not be theoretically justified as the process of reaching the sediment transport equilibrium stage is affected by the flow conditions in time, especially for fast moving flows, such as scour-hole developing flows. In this study, the two-dimensional (2D) shallow water formulation together with a sediment continuity-concentration (SCC) model were applied to flow with mobile sediment boundary. A time-varying approach was proposed to determine the sediment transport adaptation length to simulate the sediment erosion-deposition rate. The proposed computational model was based on the Finite Volume (FV) method. The Monotone Upwind Scheme of Conservative Laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate Riemann solver to discretize the FV model. In the flow applications of this paper, a highly discontinuous dam-break, fast sediment transport flow was used to calibrate the proposed time-varying sediment adaptation length model. Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in the literature, i.e. a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow. Good agreement with the experimental data were obtained with the proposed model simulations. The tests prove that the proposed model, which was calibrated by the discontinuous dam-break bed scouring flow, also performed well to represent rapid bed change and steady sediment mobility conditions.

Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.