Time evolution of the precursor wave energy given in units of upstream bulk kinetic energy: ﹩{\sigma }_{e}=3\times {10}^{-1}﹩ (left) and ﹩{\sigma }_{e}=3\times {10}^{-3}﹩ (right). In both panels, the results with our fiducial resolution (﹩{\rm{\Delta }}x/(c/{\omega }_{\mathrm{pe}})=1/40﹩) are shown by the solid lines, whereas lower resolution results (﹩{\rm{\Delta }}x/(c/{\omega }_{\mathrm{pe}})=1/20﹩) are shown by the dashed lines.