A Proper Discretization of Hydrodynamic Equations in the Cylindrical Coordinates for Astrophysical Simulations
arXiv:2012.05618 · doi:10.3847/1538-4357/abd2b2
Abstract
Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they have apparent singularity along the axis at the coordinate origin (z-axis). This singularity introduces difficulties in numerical simulations. First, it is difficult to reproduce the flow across the z-axis. Second, the time step is extremely shortened by the CFL condition near the z-axis because the numerical cell thereof is narrow in the azimuthal direction for a given angular resolution. Here, we propose a new discretization scheme to overcome these difficulties. In our new scheme, we consider changes in the direction of the unit vector within a cell when evaluating the flux across each cell surface. Besides, we evaluate the source term in the radial component of the momentum equation from the thermal and dynamic pressures working on the azimuthal cell surface. The new scheme is designed to be free-stream preserving so that flow with uniform density, pressure, and velocity isan exact solution of the discretized equation. These improvements are essential to using a lower angular resolution in the innermost area and thus to elongate each time step. Our examples demonstrate that the innermost circular region around the axis can be resolved by only six numerical cells. We present an application to an accreting compact star surrounded by a disk, in addition to Sod shock tube and rotating outflow tests.
arXiv comment24 pages, 11 figures
References in corpus (15)
- Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES
- PLUTO: a Numerical Code for Computational Astrophysics
- The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers
- Formation of Precessing Jets by Tilted Black-hole Discs in 3D General Relativistic MHD Simulations
- High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
- Testing Convergence for Global Accretion Disks
- Cloudlet capture by Transitional Disk and FU Orionis stars
- Self-gravitational Magnetohydrodynamics with Adaptive Mesh Refinement for Protostellar Collapse
- The Athena Astrophysical MHD Code in Cylindrical Geometry
- Turbulent dynamos in spherical shell segments of varying geometrical extent
- Magnetohydrodynamic Simulation Code CANS+: Assessments and Applications
- Stochastic Noncircular Motion and Outflows Driven by Magnetic Activity in the Galactic Bulge Region
- Production of intense episodic Alfvén pulses: GRMHD simulation of black hole accretion disks
- APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids
- A Possible Time-Delayed Brightening of the Sgr A* Accretion Flow after the Pericenter Passage of G2 Cloud