## 1 Introduction
When the energy density of the laser is constant, as the scanning speed increases, the depression of the melt pool will be deeper. When the scanning speed of the laser is constant, the depression will be deeper as the power increases. The size of the melt pool along the scanning direction is mainly determined by the scanning speed, and too much depression can cause abnormal flow of nearby solution, thereby increasing the tendency of pore defects. Other than the CFD method, lattice Boltzmann method (LBM) and smooth particle hydrodynamics (SPH) have been applied to simulate the melt pool. [PERSON] et al. [9] used the SPH method to establish a model considering the surface tension to observe the configuration of the melt pool. It is found that under the influence of surface tension, the longitudinal state of the melt pool changes longitudinally along the solidification track of the melt pool, and the curve is wavy. In LBM, fictive fluid particles are created at a lattice of locations which can track collisions and movement. However, there have been few applications of LBM [10] and SPH [11] to simulate the melt pool of additive manufacturing (AM) process because of lacking mature commercial software. Recently, many analytical solutions [12; 13; 14] were presented to simulate the temperature distribution and melt pool in order to optimize processing parameters and predict the part quality. Since many process parameters will affect the quality of SLM formed parts, the researchers proposed that the density of parts can be characterized by a parameter of energy density. The advantage of using energy density is that it includes parameters, such as laser power, scanning speed, layer thickness, and hatching distance, making performance evaluation and prediction easier. However, recent studies have shown that the energy density method has drawbacks [15]. For the same energy density, it may come from different parameter combinations of laser power and scanning speed, so the quality of the parts obtained is obviously different. In numerical and analytical models used to simulate a melt pool, absorptivity was usually assumed to be constant. Considering variation of the absorptivity in the process of SLM, [PERSON] (1986) calculated the absorptivity of AlSi10 Mg according to the Hagen-Ruben relationship and applied temperature-based absorptivity to FE simulation. However, it has not been applied in any analytical method. Although both of these two methods can predict the melt pool, the FE method takes a long time to obtain the calculation results. It is suitable for academic research on scientific issues and is not suitable for industrial field applications that require quick prediction. Therefore, the study of analytical methods with higher prediction accuracy has more important practical value. In this paper, we studied the absorptivity calculation of In718 material. Moreover, we recommend to determine absorptivity according to the experimental method proposed by [PERSON] (1986). As the composition of the IN718 material is more complex and the powders provided by different manufacturers have certain differences when predicting the optimal process parameters, process engineers should use the analytical method proposed in this article according to the experimental results of the powder used based on the method proposed by [PERSON] (1986). In this paper, a numerical analysis method for predicting the melt pool and defects of metal additive manufacturing is proposed. Compared with other numerical simulation methods, it is easier to operate and can quickly propose optimized process parameters. In this method, considering the actual situation of IN718's absorptivity related to temperature, laser power, scanning speed, layer thickness and other process parameters, a modified analytical solution is presented to overcome the disadvantage of existing method which viewed absorptivity as a constant, and compare it with other numerical simulation methods and experimental results for validation.