The Arbitrary accuracy Derivatives Riemann problem method(ADER) scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions: (ⅰ) Brio-Wu shock tube problem,(ⅱ) Dai-Woodward shock tube problem,(ⅲ) Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
We conduct simulations using the three-dimensional(3D)solar-interplanetary conservation element/solution element(SIP-CESE)maguetohydrodynamic(MHD)model and magnetogram data from a Carrington rotation(CR)1897 to compare the three commonly used heating methods,I.e.The Wentzel-Kramers-Brillouin(WKB)Alfvén wave heating method,the turbulence heating method and the volumetric heating method.Our results show that all three heating models can basically reproduce the bimodal structure of the solar wind observed near the solar minimum.The results also demonstrate that the major acceleration interval terminates about 4Rs for the turbulence heating method and 1ORs for both the WKB Alfvén wave heating method and the volumetric heating method.The turbulence heating and the volumetric heating methods can capture the observed changing trends by the WIND satellite,while the WKB Alfvén wave heating method does not.
