Introduction

Inland river shipping has the advantages of low cost, low energy consumption, light pollution, and large capacity. Its importance in promoting regional economic development means that countries around the world attach great significance to the development of inland river shipping. However, the increase in the number of ships leads to management problems, and extreme hydrological conditions cause ship navigation accidents, resulting in casualties and loss of property[1].Therefore, safety is increasingly the focus of attention in the shipping community.

There are many causes of shipping of the primary factors affecting the safety of shipping is the complex flow conditions caused by extreme hydrological conditions. For example, the accident of cargo ship “Yang Shi No. 8” in 1998 was caused by too high flow velocity in the waterway[2].On July 10, 2011, the passenger liner “Bu Jiaer”encountered a rainstorm in the Volga River that caused a big surge of river water to pour onto the right side of the ship, which led to its capsizing. Therefore,it is very important to obtain detailed and accurate information of the navigable flow conditions and supply an early warning, if necessary, to ensure the safety of the ship.

Currently, inland navigation relies mainly on navigation marks and electronic navigation are two problems in real applications. One is that electronic navigation charts provide only the distribution of water depth. However, research has revealed that velocity, gradient, and flow state are also important factors in the safety of navigation[3]. In an emergency, it is very important to obtain detailed,real-time navigable flow conditions to aid navigation and decision-making. The second problem is that navigation marks provide the navigable range for all ships, but each ship has different dynamic conditions and loading capacities. Thus, their suitable navigable flow conditions are not the same, and navigation marks cannot reflect this difference. Hence, providing real-time information about the current flow field distribution is important for the safety of navigation,because different ships can choose an appropriate route according to their own circumstances. In addition, detailed flow conditions can serve as an effective supplement to navigation marks, making full use of the waterway resources and improving the utilization rate of the waterway.

Previous studies on navigable flow conditions have mostly focused on approach channel, outlet area of ship lock, or parts of waterway[4-5]. Little research has considered real-time navigable flow simulations on long waterways. In navigable flow condition simulations, a 2-D hydrodynamic model can effectively simulate the flow field distribution and change processes[6-8], supplying enough flow information to the ship?s driver. The computational load of the 2-D hydrodynamic model is somewhat large, so obtaining the simulation results can take a lot of time. Although this is acceptable in waterway planning and engineering, it is not suitable for real-time navigable flow condition simulations, especially in emergency scenarios. Thus, the key point in using the 2-D hydrodynamic model for real-time navigable flow condition simulations is to improve the simulation speed and accuracy of the model. To solve the 2-D hydrodynamic model, the explicit finite volume method is widely used[9-10]. Because the discretization of friction sources takes an explicit form, the calculation of boundary fluxes uses only previous values, and there is no correlation between grid calculations in the same time step. This makes the model algorithm simpler and more effective[11].

To reduce the computation time and improve the calculation efficiency of the model, parallel computing can be applied to the 2-D hydrodynamic model[12-14]. The parallel computation of mathematical models is mainly applied in three ways: generalpurpose computing on graphics processing units, via a message processing interface, or using a shared memory architecture (OpenMP)[15-17]. In a shared memory model, communication between threads is achieved by reading and writing directly to the shared memory. Models developed in accordance with the OpenMP standard tend to be simple, extendable, and portable[18], and have obtained many good results in flood prediction and sediment transport simulations[19-20].

In this paper, a navigable flow condition simulation system to support inland river shipping is developed based on a 2-D hydrodynamic model and parallel computing technology. The main objectives of this study are to: (1) build a 2-D hydrodynamic model and study the implementation method and key technologies of 2-D hydrodynamic parallel computing based on OpenMP, (2) explore the acceleration effect of the 2-D parallel model for different meshes and hardware configurations, and (3) discuss the applications and advantages of the 2-D parallel model for inland river shipping.

1. Study area and system framework

The Yangtze River is the longest river in China,having a vast watershed area and abundant water reserves. Therefore, its navigable conditions and ship-through capacity are extensive, and it is the main focus of the development of inland shipping. Since the impoundment of the Three Gorges reservoir, shipping conditions in the upper reaches of the Yangtze River have been improved, making this region a very busy shipping line. This paper studies the waterway from Jiangjin to Chongqing, in the upper reaches of the Yangtze River (Fig. 1), a stretch of approximately 78 km,and there are nine hydrological stations along this reach. The terrain of the waterway has a large slope,and some reaches are narrow and curved. In addition,the water flow is severely affected by the Jialing River tributary. Hence, the flow conditions are very complex,making navigation difficult and leading to the occurrence of shipping accidents in recent years.