A Provable Positivity-Preserving Local Discontinuous Galerkin Method for the Viscous and Resistive MHD Equations

In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.

Influence of toroidal rotation on the tearing mode in tokamak plasmas

The stabilizing mechanism of toroidal rotation on the tearing mode is studied using the 3 D toroidal resistive magnetohydrodynamic code M3 D.It is found that the dominating mechanism,either the centrifugal effect or the Coriolis effect, depends on the specific pressure β and rotation frequency Ω.On the premise that Ω is sufficiently large, when β is greater than a critical value,the effect of the centrifugal force is dominant, and the stabilizing effect mainly comes from the modification of equilibrium induced by the centrifugal force;when β is less than a critical value,the stabilizing effect from the Coriolis force overcomes that from the centrifugal force.However,if Ω is small, then the effect of equilibrium modification due to the centrifugal force is not significant even if β is large.Finally, the results showed that toroidal rotation shear enhances the stabilizing effect.

Kinetic micro-instabilities in the presence of impurities in toroidal magnetized plasmas

The theoretical and numerical studies on kinetic micro-instabilities,including ion temperature gradient（ITG） driven modes,trapped electron modes（TEMs） in the presence of impurity ions as well as impurity modes（IMs）,induced by impurity density gradient alone,in toroidal magnetized plasmas,such as tokamak and reversed-field pinch（RFP） are reviewed briefly.The basic theory for IMs,the electrostatic instabilities in tokamak and RFP plasmas are discussed.The observations of hybrid and coexistence of the instabilities are categorized systematically.The effects of impurity ions on electromagnetic instabilities such as ITG modes,the kinetic ballooning modes（KBMs） and kinetic shear Alfvén modes induced by impurity ions in tokamak plasmas of finite β（=plasma pressure/magnetic pressure） are analyzed.The interesting topics for future investigation are suggested.

On Arbitrary-Lagrangian-Eulerian One-Step WENO Schemes for Stiff Hyperbolic Balance Laws

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.