Dongfang Liang

Solving the depth-integrated solute transport equation with a TVD-MacCormack scheme

Details are given of a numerical model for predicting solute transport in shallow waters. The alternating operator-splitting technique is used to separate the spatial discretisation of the advection and diffusion terms in each step of the time marching procedure. In the diffusion stage, a second-order accurate central scheme is used. In the advection stage, a five-point Total Variation Diminishing (TVD) modification is made to the standard MacCormack scheme. The model performance is examined by comparing numerical predictions with analytical solutions and some other numerical model results for idealised test cases. The model is also used to simulate the motion of a contaminant cloud in the River Thames estuary, where extensive wetting and drying occurs with the tidal oscillation. The present model displays sufficiently high efficiency and accuracy in solving the solute transport problems in a natural aquatic environment. It is free of fictitious oscillations close to sharp concentration gradients, while retaining second-order accuracy in smooth regions. Attention has also been paid to ensure the accurate treatment of the cross-diffusion terms and mass balance in complex flow situations.

A review on TVD schemes and a refined flux-limiter for steady-state calculations

This paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time-space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time-space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (SS-TVD). The design principles of these schemes are examined in detail. It is found that the selection of appropriate flux-limiters is a key design element in developing these schemes. Different flux-limiter forms (CFL-dependent or CFL-independent, and various limiting criteria) are shown to lead to different performances in accuracy and convergence. Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steady-state calculations based on the review. To evaluate the performance of the newly proposed scheme, many existing classical SS-TVD limiters are compared with the TCDF in eight two-dimensional test cases. The numerical results clearly show that the TCDF results in an improved overall performance.

A refined volume-of-fluid algorithm for capturing sharp fluid interfaces on arbitrary meshes

This paper presents a new volume-of-fluid scheme (M-CICSAM), capable of capturing abrupt interfaces on meshes of arbitrary topology, which is a modification to the compressive interface capturing scheme for arbitrary meshes (CICSAM) proposed in the recent literature. Without resort to any explicit interface reconstruction, M-CICSAM is able to precisely model the complex free surface deformation, such as interface rupture and coalescence. By theoretical analysis, it is shown that the modified CICSAM overcomes three inherent drawbacks of the original CICSAM, concerning the basic differencing schemes, the switching strategy between the compressive downwind and diffusive high-resolution schemes, and the far-upwind reconstruction technique on arbitrary unstructured meshes. To evaluate the performance of the newly proposed scheme, several classic interface capturing methods developed in the past decades are compared with M-CICSAM in four test problems. The numerical results clearly demonstrate that M-CICSAM produces more accurate predictions on arbitrary meshes, especially at high Courant numbers, by reducing the numerical diffusion and preserving the interface shape.

Separation of wind's influence on harmful cyanobacterial blooms.

Wind is an important physical factor involved in Harmful Cyanobacterial blooms (CyanoHABs). Its integrated influence was separated to three components: (a) Direct Disturbance Impact (DDI) on cyanbacterial proliferation, (b) Indirect Nutrient Impact (INI) by sediment release and (c) Direct Transportation Impact (DTI) by both gentle wind-induced surface drift and wave-generated Stokes drift. By the combination of field investigation, laboratory experiment and numerical simulation their individual contributions to the severe bloom event in May 2007 in Meiliang Bay, Lake Taihu, was explored. Wind synthetically made 10.5 percent promotion to the bloom on May 28, 2007, but the impact varied with locations. DTI was featured with the strongest contribution of winds impacts on CyanoHABs, while INI stood at the lowest level and DDI played an intermediate role. From the point of whole Meiliang Bay, the influencing weights of DTI, DDI and INI were approximately 48.55%, 32.30% and 19.15% respectively. DTI exerted the higher promotion in the regions of middle-east (ME), southwest (SW) and southeast (SE), and its actual contribution rate on CyanoHABs ranged from 6.41% to 7.46%. Due to the background nutrient load, INI was characterized by a tiny effect with the contribution rate being 2.18% on average. From the south bay to the north, DDI was detected with a decreasing tendency, with the practical contribution rate generally falling from 4.13% to 2.7%.

A comparison of conventional and shear-rate dependent Mohr-Coulomb models for simulating landslides

Landslides may cause many fatalities and heavy economic losses, so it is vital to understand their mechanics so as to take appropriate measures to mitigate their risk. Phenomenally, the loose soil behaves like frictional material in most circumstances, so Mohr-Coulomb type equations are often used to describe their movement. However, these models generally do not consider the influence of the shear-rate on the Mohr-Coulomb friction angle, so the shear-rate dependence effect on the soil flow and landslide runout is not well understood. This paper reports on an application of the incompressible Smoothed Particle Hydrodynamics (SPH) method to the dynamics of dry granular assemblies. The traditional model with a constant friction angle is compared with the modified Mohr-Coulomb model with a variable friction angle related to the shear-rate. It is found that the shear-rate dependence effect is negligible for shallow granular flows along mild slopes. With steeper slopes of the ground and larger aspect ratios of the initial soil column, the rate-dependence effect becomes more important.

Comparison between empirical formulae of intake vortices

The hydrodynamic properties of free surface vortices at hydraulic intakes were investigated. Based on the axisymmetric Navier–Stokes equations and empirical assumptions, two sets of formulations for the velocity distributions and the free surface profiles are proposed and validated against measurements available in the literature. Compared with previous formulae, the modifications based on Mihs formula are found to greatly improve the agreement with the experimental data. Physical model tests were also conducted to study the intake vortex of the Xiluodu hydroelectric project in China. The proposed velocity distribution formula was applied to the solid boundary as considered by the method of images. A good agreement was again observed between the prediction and the measurements.

Run-Up of Solitary Waves on Twin Conical Islands Using a Boussinesq Model

This paper investigates the interaction of solitary waves (representative of tsunamis) with idealized flat-topped conical islands. The investigation is based on simulations produced by a numerical model that solves the two-dimensional Boussinesq-type equations of Madsen and Sorensen using a total variation diminishing Lax-Wendroff scheme. After verification against published laboratory data on solitary wave run-up at a single island, the numerical model is applied to study the maximum run-up at a pair of identical conical islands located at different spacings apart for various angles of wave attack. The predicted results indicate that the maximum run-up can be attenuated or enhanced according to the position of the second island because of wave refraction, diffraction, and reflection. It is also observed that the local wave height and hence run-up can be amplified at certain gap spacing between the islands, owing to the interference between the incident waves and the reflected waves between islands.

Computation of shallow wakes with the fractional step finite element method

The depth-integrated shallow-water equations are used to simulate shallow wake flow around a solid plate-like obstacle. Influences of different terms in the equations are analyzed by normalizing the momentum equation. A fractional step finite element method is used to discretize the shallow-water equations with third-order accuracy and uniform Courant-Friedrichs-Lewy (CFL) property. The established numerical model is used to simulate the shallow wake in three typical cases and the computational flow fields are compared with digital Particle Image Velocimetry (PIV) measurements and flow visualization pictures. Three turbulence models are considered: The results of the standard k–ε model agree with the experimental results better than those of zero equation and sub-depth scale turbulence models. Furthermore, the results of the simulation also show that it is the wake stability parameter that mainly controls the flow patterns of shallow wakes.

Upscaling the shallow water model with a novel roughness formulation

This study presents a novel roughness formulation to conceptually account for microtopography and compares it to four existing roughness models from literature. The aim is to increase the grid size for computational efficiency, while capturing subgrid scale effects with the roughness formulation to prevent the loss in accuracy associated with coarse grids. All roughness approaches are implemented in the Hydroinformatics Modeling System and compared with results of a high resolution shallow water model in three test cases: rainfall-runoff on an inclined plane with sine-wave shaped microtopography, flow over an inclined plane with random microtopography and rainfall-runoff in a small natural catchment. Although the high resolution results can not be reproduced exactly by the coarse grid model, e.g. local details of flow processes can not be resolved, overall good agreement between the upscaled models and the high resolution model has been achieved. It is concluded that the accuracy increases with the number of calibration parameters available, however the calibration process becomes more difficult. Using coarser grids results in significant speedup in comparison with the high resolution simulation. In the presented test cases the speedup varies from 20 up to 2520, depending on the size and complexity of the test case and the difference in cell sizes. The proposed roughness formulation generally shows the best agreement with the reference solution, compared to the other models investigated in this study.

Numerical study of hydrodynamics of multiple tandem jets in cross flow

The hydrodynamics of a single jet and four tandem jets in a cross flow are simulated by using the Computational Fluid Dynamics (CFD) software Fluent. The realizable k - ɛ model is used to close the Reynolds-Averaged equations. The flow characteristics of the jets, including the jet trajectory, the velocity field and the turbulent kinetic energy are obtained with various jet-tocross flow velocity ratios R in the range of 2.38-17.88. It is shown that a single jet penetrates slightly deeper than the first jet in a jet group at the same R, although the difference decreases with the decrease of R. It is also found that the way in which the velocity decays along the centerline of the jet is similar for both a single jet and the first jet in a group, and the speed of the decay increases with the decrease of R. The downstream jets in a group are found to behave differently due to the sheltering effect of the first jet in the group. Compared with the first jet, the downstream jets penetrate deeper into the cross flow, and the velocity decays more slowly. The circulation zone between the two upstream jets in the front is stronger than those formed between the downstream jets. The Turbulent Kinetic Energy (TKE) sees a distinct double-peak across the cross-sections close to each nozzle, with low values in the jet core and high values in the shear layers. The double-peak gradually vanishes, as the shear layers of the jet merge further away from the nozzle, where the TKE assumes peaks at the jet centerline.