## 1 Introduction  
The shipbuilding industry is one of the supporting industries in many countries. The ship surface needs to be painted for protection. Before painting, the ship should be cleaned to make the surface be qualified to achieve the desired effect. A after a long time travelling in the river or the ocean, the ship hull surface will inevitably be covered with different coatings, which could greatly influence the travelling speed and performance of the ship. So, the ship surface should also be cleaned regularly. Surface cleaning (or coating removal) is an essential process prior to coating in the shipbuilding industry to maintain a smooth surface, minimize the fuel consumption, and extend the life span of the constructed ship [1]. Many cleaning methods have been proposed and applied for hull cleaning in the last several decades. The most widely used traditional ship surface cleaning method is called sand-blasting [2], which generates a profile in micrometer-range by accelerating a sand-blasting media through a nozzle with compressed air. However, this sand-blasting method has an obvious disadvantage: the concentration of soluble substances on the treated surface after sand-blasting is very high, and thus an extra cleaning process should be added before recoating [3]. Besides the sand-blasting method, there are also other surface preparation methods, such as high temperature oxidation [4], electrochemical method [5] and laser coating removal method [6]. The former two methods are not environmental friendly, and they both require large energy consumption, while the latter can induce thermal and physical damage to the work-piece due to excessive heat produced by the laser. Recently, hybrid laser-water-jet technology was proposed to yield high material removal rate without thermal damage [7], the energy consumption was also reduced but the costs of applying the two technologies are quite expensive. According to the literature mentioned above, the challenges faced during ship hull cleaning can be addressed as: How to minimize the energy consumption? How to realize environmental protection? How to enhance the cleaning efficiency? For the first two requirements, high speed water jet technology has been introduced recently as a promising substitute method [8]. During the water jet process, the potential energy of the high pressure water is transferred to the kinetic energy of the jet and the water jet with high velocity striking on the target can produce strong force to impact on the materials. Compared with the traditional methods, the water jet process is quite environmentally friendly, cost effective, and without abrasive contamination or heat effect zone. In the last few decades, water-jet technology has been widely used for cutting, drilling, milling [8], forming [9; 10], coating removal, and communution [11], etc. With the aim of coating removal application, extensive analyses of the water jet technology have been presented based on experiments. For example, [PERSON] et al. [3] experimentally investigated the surface quality features of one hot-rolled low-carbon steel (UH1) after high speed water jet. The roughness, hardness, and surface wettability can be increased significantly by high speed water jet profiling. [PERSON] et al. [12] adopted water jet technology to remove the heat-formed coating for Titanium alloy Ti-Al-4V. Results validated that compressive residual stress can be induced to the treated surface during the water jet process, which is beneficial to prevent stress corrosion cracking and fatigue fracturing. Even though we can visually observe the coating removal effect through experiments, the change of the high pressure water parameters, including water pressure, jet velocity, and stress distribution, during the water jet process is still a black box for us. In order to understand the water jet mechanism for coating removal in a more comprehensive way, corresponding theoretical study and numerical simulation are essential. So far, many scholars have conducted such researches.