A new numerical scheme of 3rd order Weighted Essentially Non-Oscillatory (WENO) type for 2.5D mixed GLM-MHD in Cartesian coordinates is proposed. The MHD equations are modified by combining the arguments as by Dellar ...A new numerical scheme of 3rd order Weighted Essentially Non-Oscillatory (WENO) type for 2.5D mixed GLM-MHD in Cartesian coordinates is proposed. The MHD equations are modified by combining the arguments as by Dellar and Dedner et al to couple the divergence constraint with the evolution equations using a Generalized Lagrange Multiplier (GLM). Moreover, the magnetohydrodynamic part of the GLM-MHD system is still in conservation form. Meanwhile, this method is very easy to add to an existing code since the underlying MHD solver does not have to be modified. To show the validation and capacity of its application to MHD problem modelling, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems are used to verify this new MHD code. The numerical tests for 2D Orszag and Tang's MHD vortex, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems show that the third order WENO MHD solvers are robust and yield reliable results by the new mixed GLM or the mixed EGLM correction here even if it can not be shown that how the divergence errors are transported as well as damped as done for one dimensional ideal MHD by Dedner et al.展开更多
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
This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it...This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)equations.The improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching time.Moreover,for a small CFL(say<0.1),the method can significantly reduce the numerical dissipation and retain the solution quality,which are verified by two benchmark problems.And meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme results.Finally,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.展开更多
基金Supported by the National Natural Science Foundation of China (40374056, 40536029, 40574068)the International Collaboration Research Team Program of the Chinese Academy of Sciences
文摘A new numerical scheme of 3rd order Weighted Essentially Non-Oscillatory (WENO) type for 2.5D mixed GLM-MHD in Cartesian coordinates is proposed. The MHD equations are modified by combining the arguments as by Dellar and Dedner et al to couple the divergence constraint with the evolution equations using a Generalized Lagrange Multiplier (GLM). Moreover, the magnetohydrodynamic part of the GLM-MHD system is still in conservation form. Meanwhile, this method is very easy to add to an existing code since the underlying MHD solver does not have to be modified. To show the validation and capacity of its application to MHD problem modelling, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems are used to verify this new MHD code. The numerical tests for 2D Orszag and Tang's MHD vortex, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems show that the third order WENO MHD solvers are robust and yield reliable results by the new mixed GLM or the mixed EGLM correction here even if it can not be shown that how the divergence errors are transported as well as damped as done for one dimensional ideal MHD by Dedner et al.
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 Basic Research Program of China(Grant No.2012CB825601)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-01-4)+1 种基金the National Natural Science Foundation of China(Grant Nos.41031066,41231068,41074121&41074122)the Specialized Research Fund for State Key Laboratories
文摘This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)equations.The improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching time.Moreover,for a small CFL(say<0.1),the method can significantly reduce the numerical dissipation and retain the solution quality,which are verified by two benchmark problems.And meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme results.Finally,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.
