Modeling inner boundary values at 18 solar radii during solar quiet time for global three-dimensional time-dependent magnetohydrodynamic numerical simulation

We develop an empirical model of the solar wind parameters at the inner boundary (18 solar radii, Rs) of the heliosphere that can be used in our global, three-dimensional (3D) magnetohydrodynamic (MHD) model (G3DMHD) or other equivalent ones. The model takes solar magnetic field maps at 2.5 R, which is based on the Potential Field Source Surface, PFSS model and interpolates the solar wind plasma and field out to 18 Rs using the algorithm of Wang and Sheeley (1990). A formula (V18Rs = V1 + V2fsα) is used to calculate the solar wind speed at 18 Rs, where V1 is in a range of 150–350 km s−1, V2 is in the range of 250–500 km s−1, and “fs” is the magnetic flux expansion factor derived from the Wang and Sheeley (WS) algorithm at 2.5 R. To estimate the solar wind density and temperature at 18 Rs, we assume an incompressible solar wind and a constant total pressure. The three free parameters are obtained by adjusting simulation results to match in-situ observations (Wind) for more than 54 combinations of V1, V2 and α during a quiet solar wind interval, i.e., the Carrington Rotation (CR) 2082. We found that VBF = (200 ± 50) + (400 ± 100) fs−0.4 km/s is a good formula for the quiet solar wind period. The formula was also good to use for the other quiet solar periods. Comparing results between WSA (Arge et al. 2000, 2004) and our model (WSW-3DMHD), we find the following: i) The results of using VBF with the full rotation (FR) data as input to drive the 3DMHD model is better than the results of WSA using FR, or daily updated. . ii) The WSA model using the modified daily updated 4-day-advanced solar wind speed predictions is slightly better than that for WSW-3DMHD. iii) The results of using VBF as input to drive the 3DMHD model is much better than the using the WSA formula with an extra parameter for the angular width (θb) from the nearest coronal hole. The present study puts in doubt in the usefulness of θb for these purposes. •We develop an empirical model of the solar wind parameters at the inner boundary (18 solar radii) of the heliosphere that can be used in our global, three-dimensional (3D) magnetohydrodynamic (MHD) model (G3DMHD) or other equivalent ones.•We found that VBF = (200±50) + (400±100) fs-0.4 km/s is a good formula for the quiet solar wind period. The formula was also good to use for the other quiet solar periods. Comparing results between WSA (Arge et al. 2000; 2004) and our model (WSW-3DMHD). * VBF : Best Fit Velocity formula.•The results of using VB