[P-EM17] Space Plasma Science

[PEM17-P03] Relaxation of the Courant Condition and Reduction of Numerical Errors in the Explicit Finite-Difference Time-Domain Method

*Harune Sekido^1,2, Takayuki Umeda³, Yoshizumi Miyoshi² (1.Graduate School of Engineering, Nagoya University, 2.Institute for Space-Earth Environmental Research, Nagoya University, 3.information initiative center, Hokkaido University)

Keywords:FDTD, Courant condition, dispersion relation, phase velocity, Laplacian, anisotropy

This study provides a new numerical method for relaxation of the Courant condition and correction of numerical errors in the Finite-Difference Time-Domain (FDTD) method with the time-development equations using higher-degree difference terms. The FDTD method (Yee 1966) is a numerical method for solving the time development of electromagnetic fields by approximating Maxwell's equations in both space and time with the finite difference of the second-order accuracy. Numerical oscillations occur due to the error between the numerical phase velocity and the theoretical phase velocity. The FDTD(2,4) method (Fang 1989; Petropoulos 1994), which uses the fourth-order spatial difference, is proposed for reduction of the numerical errors. However, the Courant condition becomes more restricted by using higher-order finite differences in space and a larger number of dimensions. Recently, a numerical method has been developed by adding third-degree difference terms to the time-development equations of FDTD(2,4) (Sekido & Umeda, IEEE TAP, 2023), which relaxes the Courant condition, although there exist large numerical errors with large Courant numbers. In the present study, a new explicit and non-dissipative FDTD method is proposed with two types of the higher-degree difference operators for relaxation of the Courant condition and reduction of numerical errors. First, the one-dimensional third- and fifth-degree difference terms are added to the time-development equations of FDTD(2,6) (Sekido & Umeda, PIER M, 2024). Second, the third-degree difference terms including Laplacian are added to those of FDTD(2,4) (Sekido & Umeda, EPS, 2024). Both of these schemes are stable with large Courant numbers up to 1. The results of the test simulations show that numerical oscillations are not reduced so much with the one-dimensional difference operator, whereas the Laplacian operator suppresses an anisotropy in the waveforms and reduces the numerical oscillations.