The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations ap-ized to include the modeling of curved surfaces [8][9] and plied to the Maxwell equations on multi-dimensional grids. Both body oriented grids [10][11][12][13]. It is currently one of the most Cartesian grids and non-Cartesian grids based on hexagons and successful techniques in CEM. More recently, the progress tetradecahedra are studied and compared. The numerical errors are in interdisciplinary computational physics has created a quantitatively determined in terms of phase speed, wavenumber, new approach that uses numerical algorithms developed propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient and accurate than for solving the fluid flow equations in computational fluid upwind schemes and the non-Cartesian grids yield superior isotropy dynamics (CFD) to solve the time-domain Maxwell equathan the Cartesian ones. For the centered schemes, the staggered tions. Shankar et al. were the first to introduce this type grids produce less errors than the unstaggered ones. A new unstagof approach and coined it a CFD-based method [14][15].
gered algorithm which has all the best properties is introduced.
The method employs an upwind Riemann solver and the
Using an optimization technique to determine the nodal weights, the new algorithm provides the highest accuracy among all the Lax-Wendroff time integration in a finite-volume formulaschemes discussed. The study also demonstrates that a proper tion. It is also a successful technique in CEM. choice of time discretization can reduce the overall numerical errors Numerical approximations inevitably introduce errors. due to the spatial discretization.