## 2 Materials and Methods
### Used Particle Properties  
Alumina also referred to as aluminium oxide (Al\({}_{2}\)O\({}_{3}\)), has exceptional qualities such as hardness, wear resistance, and chemical inertness, making it a premier choice for various industrial applications involving abrasion. In the field of grinding tools, alumina is a standout choice, serving as either an abrasive grain or a crucial component in abrasive formulations. Alongside alumina, a diverse range of abrasive materials, including silicon carbide, diamond, cubic boron nitride, and corundum, plays a significant role in this sector. The applications of aluminium oxide are extensive, spanning from wear protection coatings in machines and plants to corrosion protection in the chemical industry. Additionally, it finds use as insulation material in electronics and high-temperature applications. The suitability of aluminium oxide, corundum, and other materials depends on factors such as their content, grain size, and porosity, all of which are decisive for their specific areas of application in diverse industrial scenarios involving abrasion, wear protection, and corrosion resistance [35, 36]. Particle Shape and Size Distribution  
The potential for modelling at the particle level is a key advantage of the Discrete Element Method (DEM). However, real-world applications encounter a significant challenge due to the uncontrollable increase in number of particles. These systems, often comprising millions or even billions of individual particles, result in computationally expensive simulations that are frequently impractical. As computational capabilities have advanced, more complex non-spherical shapes have been incorporated using various techniques [32]. It's essential to note that the particle shape and size significantly impact all other model parameters requiring calibration and should be the initial consideration when conducting numerical simulations. In the case of conducting numerical simulations of abrasive powders (Figure 2), physical particles exhibit non-spherical shapes. Accurately characterizing these shapes remains exceedingly difficult due to their irregular nature. Due to a lack of computing resources, we implemented  
Coarse graining (CGM) is the process of simplifying a system by representing groups of fine-scale particles or degrees of freedom with fewer, coarser-scale entities, necessitating adjustments to the contact model while maintaining similarity to the original system [37]. The particle group has a unique scale factor \(f_{CGM}\) that determines the parcel size and the  
Figure 2: A representative sample of abrasive alumina particles, with an average size of 150 \(\upmu\)m, as viewed under the microscope. number of original particles represented. The aim is to maintain the same energy density and the evolution of energy density as per the real base model with real particle size distribution. The CGM approach utilized by [PERSON] is founded on the research conducted by [PERSON] et al. (2018). The scale factor utilizes multiplication to increase the original particle size from Figure 3, defining the new parcel size and, consequently, determining the number of original particles the parcel represents. The gravitational potential energy density remains constant regardless of the particle diameter as long as the solid density and the volume fraction of the particles remain unchanged. In order to maintain the conservation of kinetic energy variation \(\Delta E_{kin}\), the velocity variation of a scaled-up system for the relative velocities of the particles before (\(v_{a}\)) and after the contact (\(v_{b}\)) with a constant effective contact mass \(m^{*}\) must remain equal to that of the original system during contact. \[\Delta E_{kin}=\frac{m^{*}}{2}\cdot\left(v_{b}^{2}-v_{a}^{2}\right) \tag{6}\]  
Continuing, dimension analysis and adjustments to all contact parameters, including but not limited to contact stiffness and damping coefficients, are necessary to ensure compatibility with the coarse-grained model.