MHD modelling in space weather: Accuracy issues

MHD numerical models are often used in many studies of relatively large spatial and temporal scales in space weather. In this study, we present how accuracy and precision can quantitatively be estimated in time-dependent MHD simulations. We adopt an exact solution of full MHD equations that we have obtained by utilizing the concept of simple waves. By comparing MHD simulations with this analytical solution, which allows arbitrary source motion, it is shown that our exact solutions are consistent with numerical solutions when both spatial and temporal resolution gradually increase in the numerical model. When we apply the MHD model to the Sun-Earth space weather issues such as CME propagation, it is found that numerical errors in such long distance simulations are unavoidable, and full attention to the model parameters is required to maintain simulations with a certain level of accuracy. Our MHD simulation tests for CMEs, based on the grid resolution of N=100 100,000 over the interval of 1AU, explicitly show how there occur significant computational errors such as up to 5-15 hrs in arrival timing at the Earth, in the model of the similar resolution used in current operation models (e.g., N=128 512 over 1AU). Those error values are found to be consistent with current observational feature. We present how pure computational errors can be affected and modified in a quantitative manner by examining different types of CMEs and model parameters. It is suggested that our results will be of great importance in optimizing simulation parameters differentially for each individual event in advance to avoid large numerical errors in the current operation-oriented MHD models.