The high-order, low dissipation Euler flux method of Fisher et al. [1] is implemented in the CFD code Eilmer for the purpose of direct numerical simulations of boundary layer transition. Measurements of numerical dissipation and dispersion errors are performed on the isentropic vortex, and a new test problem is introduced to measure numerical dissipation as a function of wavenumber. The high-order method is shown to perform significantly better than the traditional Riemann-based flux methods in regards to both dissipation and dispersion. Additionally, it is shown that improving the accuracy of left and right Riemann state reconstructions has limited effect on numerical dispersion.