Time-dependent numerical modeling of large-scale astrophysical processes: from relatively smooth flows to explosive events with extremely large discontinuities and high Mach numbers

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Authors

KURFÜRST Petr KRTIČKA Jiří

Year of publication 2017
Type Article in Periodical
Magazine / Source Applications of Mathematics
MU Faculty or unit

Faculty of Science

Citation
Web
Doi http://dx.doi.org/10.21136/AM.2017.0135-17
Field General mathematics
Keywords Eulerian hydrodynamics; finite volume; operator-split method; unsplit method; Roe's method; curvilinear coordinates
Description We calculate self-consistent time-dependent models of astrophysical processes. We have developed two types of our own (magneto) hydrodynamic codes, either the operator-split, finite volume Eulerian code on a staggered grid for smooth hydrodynamic flows, or the finite volume unsplit code based on the Roe's method for explosive events with extremely large discontinuities and highly supersonic outbursts. Both the types of the codes use the second order Navier-Stokes viscosity to realistically model the viscous and dissipative effects. They are transformed to all basic orthogonal curvilinear coordinate systems as well as to a special non-orthogonal geometric system that fits to modeling of astrophysical disks. We describe mathematical background of our codes and their implementation for astrophysical simulations, including choice of initial and boundary conditions. We demonstrate some calculated models and compare the practical usage of numerically different types of codes.
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