4 research outputs found
Numerical comparison of Riemann solvers for astrophysical hydrodynamics
The idea of this work is to compare a new positive and entropy stable
approximate Riemann solver by Francois Bouchut with a state-of the-art
algorithm for astrophysical fluid dynamics. We implemented the new Riemann
solver into an astrophysical PPM-code, the Prometheus code, and also made a
version with a different, more theoretically grounded higher order algorithm
than PPM. We present shock tube tests, two-dimensional instability tests and
forced turbulence simulations in three dimensions. We find subtle differences
between the codes in the shock tube tests, and in the statistics of the
turbulence simulations. The new Riemann solver increases the computational
speed without significant loss of accuracy.Comment: 24 pages, 38 figures. To be published in Journal of Computational
Physic
A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests
The ideal MHD equations are a central model in astrophysics, and their
solution relies upon stable numerical schemes. We present an implementation of
a new method, which possesses excellent stability properties. Numerical tests
demonstrate that the theoretical stability properties are valid in practice
with negligible compromises to accuracy. The result is a highly robust scheme
with state-of-the-art efficiency. The scheme's robustness is due to entropy
stability, positivity and properly discretised Powell terms. The implementation
takes the form of a modification of the MHD module in the FLASH code, an
adaptive mesh refinement code. We compare the new scheme with the standard
FLASH implementation for MHD. Results show comparable accuracy to standard
FLASH with the Roe solver, but highly improved efficiency and stability,
particularly for high Mach number flows and low plasma beta. The tests include
1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We
consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas
flows in the interstellar medium. We investigate both strong initial magnetic
fields and magnetic field amplification by the turbulent dynamo from extremely
high plasma beta. The energy spectra show a reasonable decrease in dissipation
with grid refinement, and at a resolution of 512^3 grid cells we identify a
narrow inertial range with the expected power-law scaling. The turbulent dynamo
exhibits exponential growth of magnetic pressure, with the growth rate twice as
high from solenoidal forcing than from compressive forcing. Two versions of the
new scheme are presented, using relaxation-based 3-wave and 5-wave approximate
Riemann solvers, respectively. The 5-wave solver is more accurate in some
cases, and its computational cost is close to the 3-wave solver.Comment: 26 pages, 17 figures, Journal of Computational Physics, publishe
NUMERICAL COMPARISON OF RIEMANN SOLVERS FOR ASTROPHYSICAL HYDRODYNAMICS
Abstract. The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with state-of the-art algorithms for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy. 1
NUMERICAL COMPARISON OF RIEMANN SOLVERS FOR ASTROPHYSICAL HYDRODYNAMICS
Abstract. The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy. 1