Top, far left: distribution of the reference solution of the velocity u_z,H in a restricted domain along the y direction (y ∈ [0.2, 0.8] Mm) in km s⁻¹. Top, center and right: two-dimensional figures representing represent the logarithm of the difference between the reference and the numerical solution ${\log }_{10}(u_{z,H}^{ref}-u_{z,H})$ for PIROCK with tolerance 10⁻⁵, 10⁻², splitting, and explicit. Bottom: one-dimensional distribution ${\log }_{10}(u_{z,H}^{ref}-u_{z,H})$ of all these cases at y = 0.5 Mm and z ∈ [1.5, 3] Mm at t = 50 s.