ADER-WENO Schemes the 2D MuSIC Riemann solver. Figure 6 shows the same Alfven wave propagation test. This time, we used different ADER-WENO schemes with increasing order of accuracy. We also used the 1D HLLI Riemann solver along with the 2D MuSIC Riemann solver with sub-structure. We see that higher order schemes produce lower dissipation.