Abstract
In this chapter, we describe in detail an efficient, high-resolution and oscillation-free hybrid scheme for shock-turbulence interactions in compressible MHD problems. The hybrid scheme couples compact finite difference scheme with WENO scheme, wherein compact finite difference scheme used in the smooth region ensures the accuracy, while WENO scheme applied in the shock region captures discontinuities robustly. In order to maintain numerical stability and eliminate spurious oscillations, we utilize a pentadiagonal filter.
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References
Balsara DS, Kim J (2004) A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics. Astrophys J 602:1079–1090
Biskamp D (2003) Magnetohydrodynamic turbulence. Cambridge University Press, Cambridge
Gaitonde DV, Visbal MR (1998) High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. Technical Report AFRL-VA-WP-TR-1998-3060, US Air Force Research Laboratory, Wright-Patterson AFB
Gear CW (1971) Numerical initial value problems in ordinary differential equations. Prentice Hall PTR
Hirsch C (2007) Numerical computation of internal and external flows: fundamentals of computational fluid dynamics. Butterworth-Heinemann
Jiang GS, Wu CC (1999) A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. J Comput Phys 150:561–594
Kawai S (2013) Divergence-free-preserving high-order schemes for magnetohydrodynamics: an artificial magnetic resistivity method. J Comput Phys 251:292–318
Kim JW (2010) High-order compact filters with variable cut-off wavenumber and stable boundary treatment. Comput Fluids 39:1168–1182
Lambert JD (1973) Computational methods in ordinary differential equations. Wiley
Lele SK (1992) Compact finite difference schemes with spectral-like resolution. J Comput Phys 103:16–42
Müller WC, Biskamp D (2000) Scaling properties of three-dimensional magnetohydrodynmaic turbulence. Phys Rev Lett 84:475
Shen Y, Zha G, Huerta MA (2012) E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO scheme. J Comput Phys 231:6233–6247
Shu CW, Osher S (1988) Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys 77:439–471
Tóth G (2000) The \(\nabla \cdot \mathbf{B}=0\) constraint in shock-capturing magnetohydrodynamics codes. J Comput Phys 161:605–652
Van Der Houwen PJ (2012) Construction of integration formulas for initial value problems, vol 19. Elsevier
Wang J, Wang LP, Xiao Z, Shi Y, Chen S (2010) A hybrid numerical simulation of isotropic compressible turbulence. J Comput Phys 229:5257–5279
Wang J, Yang Y, Shi Y, Xiao Z, He XT, Chen S (2013) Cascade of kinetic energy in three-dimensional compressible turbulence. Phys Rev Lett 110:214–505
Yang Y, Wan M, Shi Y, Yang K, Chen S (2016) A hybrid scheme for compressible magnetohydrodynamic turbulence. J Comput Phys 306:73–91
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Yang, Y. (2019). Hybrid Scheme for Compressible MHD Turbulence. In: Energy Transfer and Dissipation in Plasma Turbulence . Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-13-8149-2_3
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DOI: https://doi.org/10.1007/978-981-13-8149-2_3
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Online ISBN: 978-981-13-8149-2
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