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|Title: ||Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes.|
|Authors: ||Balbas, Jorge|
|Keywords: ||multidimensional conservation laws|
ideal magnetohydrodynamics (MHD) equations
high-resolution central schemes
|Issue Date: ||2006|
|Publisher: ||Copyright: Society for Industrial and Applied Mathematics|
|Citation: ||J. Balbas & E. Tadmor (2006). Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes. SIAM Journal on Scientific Computing 28 (2006) 533-560.|
|Abstract: ||We present a new family of high-resolution, nonoscillatory semidiscrete central
schemes for the approximate solution of the ideal magnetohydrodynamics (MHD) equations. This
is the second part of our work, where we are passing from the fully discrete staggered schemes in [J.
Balb´as, E. Tadmor, and C.-C. Wu, J. Comput. Phys., 201 (2004), pp. 261–285] to the semidiscrete
formulation advocated in [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 241–282].
This semidiscrete formulation retains the simplicity of fully discrete central schemes while enhancing
efficiency and adding versatility. The semidiscrete algorithm offers a wider range of options to implement
its two key steps: nonoscillatory reconstruction of point values followed by the evolution of the
corresponding point valued fluxes. We present the solution of several prototype MHD problems. Solutions
of one-dimensional Brio–Wu shock-tube problems and the two-dimensional Kelvin–Helmholtz
instability, Orszag–Tang vortex system, and the disruption of a high density cloud by a strong shock
are carried out using third- and fourth-order central schemes based on the central WENO reconstructions.
These results complement those presented in our earlier work and confirm the remarkable
versatility and simplicity of central schemes as black-box, Jacobian-free MHD solvers. Furthermore,
our numerical experiments demonstrate that this family of semidiscrete central schemes preserves the
∇ · B = 0-constraint within machine round-off error; happily, no constrained-transport enforcement
|Appears in Collections:||Mathematics Research Works|
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