## 1 Introduction  
Formation of micro defects during solidification processes has gained the attention of many researchers since they affect the mechanical properties of solidified components [1; 2; 3]. Numerous attempts have been made to minimize porosity in castings [4; 5; 6]. For example, understanding bubble formation and motion during dendritic solidification would help to improve the quality of cast products [7]. In-situ observation provides useful information about the bubble formation and morphology during solidification. Several methods are available to observe porosity during solidification, such as optical methods [8; 9] and micro focus X-ray imaging [10; 11; 12]. Generally, in-situ experiments suffer from limitations regarding tracking the bubble motion, transparency of alloys, and the thickness of sample [13]. Numerical simulations offer an alternative to investigate the mechanism behind bubble formation and their interactions during solidification of metallic alloys. [PERSON] et al. [14] proposed a hybrid level set enthalpy-based model to simulate the evolution of hydrogen bubbles during the solidification of aluminum alloys in 2D. They estimated the final pore shape based on the pore radius and cooling rate. [PERSON] et al. [15] simulated the evolution of porosity for Al-Si. They identified three zones in the domain. In zone one, a small-sized porosity was observed. In zone two, which they called the transition zone, the porosity was elongated. In zone three or the central zone, the pores are rounded. [PERSON] et al. [16] simulated the dendritic growth in pure aluminum with pre-existing pores using the phase field method. They presented the effects of pressure on gas bubble formation, nucleation, and evolution. They modeled and discussed the interaction between bubbles and the solid-liquid interface. They showed that the presence of gas bubbles in solid-liquid interfaces could change the dendritic growth significantly. One of the challenges in modeling bubble dynamics during dendritic growth is how to simulate multiphase flow. Bubble dynamics simulations are often very computationally demanding. One reason for the cost is the difficulty regarding tracking the interface between different phases. Conventional computational fluid dynamics (CFD) models to solve multiphase flow are divided into two main categories: Interface tracking methods and interface capturing methods. In interface tracking methods, the location of the interface is marked with a separate grid or set of surface meshes from an initial condition and calculated explicitly during the simulation. The boundary integral methods [17], the arbitrary Lagrangian-Eulerian (ALE) method [18], and all front tracking methods [19; 20; 21; 22; 23; 24] belong to this category. In interface capturing methods, instead of tracking a sharp interface, a function represents the thin, but non-zero, interface between phases. This leads to the fluid properties changing continuously from one fluid to another across the interface. The volume of fluid (VOF), phase field, and level set methods belong to this category [25; 26; 27]. As an alternative to more conventional methods, the lattice Boltzmann (LB) method is successfully used in many different multiphase problems [28; 29]. The LB method, with its roots in kinetic theory, is based on a solution of the Boltzmann kinetic equation for a group of imaginary particles in a discretized domain, which can recover the Navier-Stokes equation. Therefore, LB retrieves macroscopic properties of the fluid while making use of the microscopic method. Due to its simplicity, local structure, ease in dealing with complex geometries, explicit nature, and suitability to use in distributed memory architectures, it has been applied to simulate various physical phenomena [13; 28; 30; 31].