Schematic illustration of the mesh concerning RT. The left panel shows the computational meshes employed for solving the governing equations in the MURaM code, while the right panel illustrates the relationship between the radiation ray and the mesh structure. The MHD mesh is employed for solving the MHD equations, whereas the RT mesh is used for solving the RT equation. Both meshes are uniform and Cartesian, with the RT grid points positioned at the centers of the cells formed by adjacent MHD grid points. Information exchange between the two meshes is accomplished through bi-linear or tri-linear interpolation. Rays are involved in solving the RT equation using the short-characteristics method, in which the ray intensity at the grid points (o) is the quantity being solved for in MURaM. The solution involves the source functions at the upwind (u), downwind (d), and grid points, along with the ray intensity at the upwind point. The rays typically do not intersect with the grid vertices. Linear or bi-linear interpolation was employed to compute the source function, opacity, and ray intensity at the upwind and downwind points.