Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
An HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
A Class of Extended Limiters Applied to Piecewise Hyperbolic Methods
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
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In this paper we perform an analysis of the wave structure of the ideal magnetohydrodynamic (MHD) equations. We present an analytical expression of the nonlinearity term associated to each characteristic field derived from a scaled version of the complete system of eigenvectors proposed by Brio and Wu [M. Brio, C.C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys. 75 (2) (1988) 400-422] and adopting the eight wave approach by Powell et al. [K.G. Powell, P.L. Roe, R.S. Myong, T. Gombosi, D. deZeeuw, An upwind scheme for magnetohydrodynamics, AIAA 12th Computational Fluid Dynamics Conference, San Diego, CA, 1995, pp. 661-674]. A criterion for the detection of local regions containing points for which a nonlinear characteristic field becomes nonconvex is formulated for the two-dimensional case. We then design a characteristic-based upwind scheme for the ideal MHD equations that resolves the wave dynamics by local characteristic wavefields. The new scheme is able to detect local regions containing nonconvex singularities and to handle an entropy correction through a prescription of a local viscosity ensuring convergence to the entropy solution. A third order accurate version of the scheme performs satisfactorily in resolving one and two-dimensional MHD problems. Numerical results indicate that the proposed scheme behaves low dissipative, stable and accurate under high CFL numbers.