A Runge-Kutta-Gegenbauer super-time-stepping method for stable, efficient handling of anisotropic non-ideal MHD diffusion.
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.
representative citing papers
Restarted jets propagate ballistically through rarefied remnant cocoons with minimal backflow, decelerating only at dense entrained structures, after the cocoon evolves through conical-cylindrical-mushroom phases shaped by KH/RT entrainment.
Multi-dimensional simulations show that the parameter space for shocks in non-dissipative transonic sub-Keplerian accretion flows is substantially larger than the analytic prediction, with dynamic boundary layers producing outflows.
For a 9.6 solar mass supernova, including scattered halo neutrinos delays the onset of collective neutrino oscillation at early times and sharpens spectral swap features, improving their detectability.
A hybrid conical/vertical-equilibrium disc geometry improves agreement with simulations of shocked black hole accretion, and shock-infall timescales reproduce observed QPO frequencies across ten Galactic X-ray binaries.
A GRHD finite-volume code is validated against analytic transonic solutions and applied to 2D sub-Keplerian accretion, recovering shocks and frame-dragging effects.
citing papers explorer
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A robust super-time-stepping scheme for Ohmic and ambipolar diffusion
A Runge-Kutta-Gegenbauer super-time-stepping method for stable, efficient handling of anisotropic non-ideal MHD diffusion.
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Numerical Simulations of Restarted Jets -- I. Dynamics
Restarted jets propagate ballistically through rarefied remnant cocoons with minimal backflow, decelerating only at dense entrained structures, after the cocoon evolves through conical-cylindrical-mushroom phases shaped by KH/RT entrainment.
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Simulation based parameter space for shock in transonic, sub-Keplerian accretion flow onto non-rotating black holes
Multi-dimensional simulations show that the parameter space for shocks in non-dissipative transonic sub-Keplerian accretion flows is substantially larger than the analytic prediction, with dynamic boundary layers producing outflows.
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Neutrino halo effect on collective neutrino oscillation in iron core-collapse supernova model of a 9.6 $M_{\odot}$ star
For a 9.6 solar mass supernova, including scattered halo neutrinos delays the onset of collective neutrino oscillation at early times and sharpens spectral swap features, improving their detectability.
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Hybrid disc geometry for shocked accretion flows: Unveiling QPOs in black hole X-ray binaries
A hybrid conical/vertical-equilibrium disc geometry improves agreement with simulations of shocked black hole accretion, and shock-infall timescales reproduce observed QPO frequencies across ten Galactic X-ray binaries.
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A general relativistic hydrodynamic simulation code for studying advective, sub-Keplerian accretion flow onto black holes
A GRHD finite-volume code is validated against analytic transonic solutions and applied to 2D sub-Keplerian accretion, recovering shocks and frame-dragging effects.