Abstract
Abstract We present a new magnetohydrodynamic (MHD) simulation package with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the Harten–Lax–van Leer–discontinuitues (HLLD) approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation (MP5) scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes has significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems show the advantages of using the high-order scheme by comparing with results from a standard second-order total variation diminishing monotonic upwind scheme for conservation laws (MUSCL) scheme. The present code enables us to explore the long-term evolution of a three-dimensional accretion disk around a black hole, in which compressible MHD turbulence causes continuous mass accretion via nonlinear growth of the magneto-rotational instability (MRI). Numerical tests with various computational cell sizes exhibits a convergent picture of the early nonlinear growth of the MRI in a global model, and indicates that the MP5 scheme has more than twice the resolution of the MUSCL scheme in practical applications.
Highlights
In the last decades, computational astrophysics has emerged together with the rapid growth of computational capabilities, enabling us to reveal various aspects of astrophysical phenomena that cannot be provided by observations
All of these mechanisms were successfully solved by adopting the HLLD approximate Riemann solver, the MP5 reconstruction, and the hyperbolic divergence cleaning method in CANS+
We have developed CANS+, a high-resolution, numerically robust MHD simulation code by employing the HLLD approximate Riemann solver, the MP5 reconstruction method, and the hyperbolic divergence cleaning method
Summary
Computational astrophysics has emerged together with the rapid growth of computational capabilities, enabling us to reveal various aspects of astrophysical phenomena that cannot be provided by observations. The systems are dominated by various MHD discontinuities, shock waves, and turbulence in which the fluid dynamics are strongly coupled with the magnetic field Such highly nonlinear systems have stimulated the search for numerical algorithms that can solve the MHD equations with both high accuracy and stability. Modern MHD simulation codes have a strategy of accurately capturing shock waves as situations often accompany with supersonic flows in space and astrophysical phenomena Such shockcapturing schemes are based on the finite volume method in which the time evolution of cell-averaged conservative variables of the MHD equations is calculated from numerical fluxes at the cell surfaces. Waves of the ideal MHD system, the GLM–MHD system introduces two waves with the eigenvalues (phase speeds) of λ1,9 = ∓ch, which represent omnidirectional propagation of numerical errors of the divergence-free condition (equation (9))
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