An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Abstract

Abstract.A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and efficient central scheme described in Paper I (Del Zanna & Bucciantini 2002) for relativistic hydrodynamics is here extended to the magnetic case by following the strategies prescribed for classical MHD by Londrillo & Del Zanna (2000). The scheme completely avoids spectral decomposition into characteristic waves, which is computationally expensive and subject to many degenerate cases in the magnetic case, while it makes use of a two-speed Riemann solver that just requires the knowledge of the two local fast magnetosonic velocities. Moreover, the onset of spurious magnetic monopoles, which is a typical problem for multi-dimensional MHD upwind codes, is prevented by properly taking into account the solenoidal constraint and the specific antisymmetric nature of the induction equation. Finally, the extension to generalized orthogonal curvilinear coordinate systems is included, thus the scheme is ready to incorporate general relativistic (GRMHD) effects.

3D MHD simulations of magnetic field evolution and radio polarization of barred galaxies

“…All calculations were performed using the Godunov code ) based on the essentially non-oscillatory (ENO) spatial reconstruction, Harten-Lax-van-Leer (HLL) approximate Riemann-solver, Runge-Kutta (RK) time integration (Del Zanna et al 2003) to solve isothermal MHD equations, and constrained transport method (Evans & Hawley 1988) to keep a zero magnetic field divergence. The computational domain covers 30 kpc × 30 kpc × 7.5 kpc of space with 512×512×128 cells of a 3D cartesian grid, which yields about 60 pc of spatial resolution in each direction.…”

Magnetohydrodynamics in full general relativity: Formulation and tests

“…In this case, roughly speaking, there are two options for numerically handling the transport terms [38]. One is to use the Godunov-type, approximate Riemann solver [39,40], and the other is to use the high-resolution central (HRC) scheme [41,20]. We adopt a HRC scheme proposed by Kurganov and Tadmor [42] and very recently used in special relativistic simulations by LucasSarrano et al [43].…”

“…The parameters for the initial conditions adopted here are the same as those in [41]. On the other hand, we varied the grid spacing to see the convergence in contrast to the previous works.…”

Three-dimensional simulations of compressible tearing instability

“…31 and 32. A related version of the code has been designed for special relativistic 33 and general relativistic ideal MHD equations. 34 With respect to previous versions, in the code an explicit plasma resistivity has been introduced and space resolution has been improved by using high-order compact ͑or implicit͒ difference schemes 30 to approximate flux derivatives.…”