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...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.展开更多
Three modes of magnetic reconnection,flux pile-up,Sonnerup,and hybrid,are examined in the context of driven magnetic reconnection via 2D and 2.5D magnetohydrodynamic(MHD)numerical simulations.They result from variance...Three modes of magnetic reconnection,flux pile-up,Sonnerup,and hybrid,are examined in the context of driven magnetic reconnection via 2D and 2.5D magnetohydrodynamic(MHD)numerical simulations.They result from variances in gas pressure and magnetic field strength in the reconnection inflow region.The simulation demonstrates that the Spitzer diffusion region of magnetic reconnection is not just an X-point;instead,it appears as a slim and elongated current sheet that creates two pairs of the slow-mode shock(SS)on either end.These shocks contribute to forming four boundaries that separate the inflow from the outflow.In the regions far from the Spitzer diffusion region,two sets of rotational discontinuity(RD)stand inside the SSs and form the combination of SS and RD structures.The RDs reverse the magnetic field inside the reconnection outflow region,and create a W-shaped magnetic field in that region.The scenario that the rotation of the magnetic field is not caused by an intermediate wave,and the SS is located outside the RD,is consistent with the inference of Priest(Mon.Not.R.Astron.Soc.159,389(1972)),and is contrary to that of Petschek and Thorne(Astrophys.J.147,1157(1967))and Vasyliunas(Rev.Geophys.Space Phys.13,303(1975)).展开更多
基金Supported by the National Natural Science Foundation of China(40904050,40874077)the Specialized Research Fund for State Key Laboratories
文摘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.
基金supported by the National Key R&D Program of China(Grant No.2022YFF0503804)the National Natural Science Foundation of China(Grant Nos.11933009,12273107,and U2031141)+2 种基金the Applied Basic Research of Yunnan Province(Grant No.2019FB005)the Yunnan Province Scientist Workshop of Solar Physicsthe Yunnan Province Yunling Scholar Project.
文摘Three modes of magnetic reconnection,flux pile-up,Sonnerup,and hybrid,are examined in the context of driven magnetic reconnection via 2D and 2.5D magnetohydrodynamic(MHD)numerical simulations.They result from variances in gas pressure and magnetic field strength in the reconnection inflow region.The simulation demonstrates that the Spitzer diffusion region of magnetic reconnection is not just an X-point;instead,it appears as a slim and elongated current sheet that creates two pairs of the slow-mode shock(SS)on either end.These shocks contribute to forming four boundaries that separate the inflow from the outflow.In the regions far from the Spitzer diffusion region,two sets of rotational discontinuity(RD)stand inside the SSs and form the combination of SS and RD structures.The RDs reverse the magnetic field inside the reconnection outflow region,and create a W-shaped magnetic field in that region.The scenario that the rotation of the magnetic field is not caused by an intermediate wave,and the SS is located outside the RD,is consistent with the inference of Priest(Mon.Not.R.Astron.Soc.159,389(1972)),and is contrary to that of Petschek and Thorne(Astrophys.J.147,1157(1967))and Vasyliunas(Rev.Geophys.Space Phys.13,303(1975)).
