Time evolution of the y-direction kinetic energy rescaled by its initial value in the magnetized Kelvin–Helmholtz instability test problem. Each panel corresponds to a different initial Mach number, ℳ_x. Different colors are used for different grid resolutions (the 64 × 32 and 128 × 64 grids cells have been left out for clarity). Results obtained with the HLLD solver are represented by dot-dashed lines, while solid lines are used for LHLLD. The solid black line in each panel is the reference solution. As explained in the text, the nonlinear solver does not converge when using HLLD at ℳ_x = 10⁻⁴ for N > 64.