RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code. We have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite-difference, weighted essentially nonoscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth-order accuracy in space. For time integration we use the method of lines with a third-order total variation diminishing (TVD) Runge-Kutta scheme. We have also implemented fourth- and fifth-order Runge-Kutta time integration schemes for comparison. The implementation of AMR and parallelization is based on the FLASH code. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods, and physics modules. In addition to WENO, we have implemented a finite-volume module with the piecewise parabolic method for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. We examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. We show that underresolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two, and three dimensions and in Cartesian, cylindrical, and spherical coordinates. We have demonstrated fifth-order accuracy for WENO in one and two dimensions and performed detailed comparison with other schemes for which we show significantly lower convergence rates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics.

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  1. Bhoriya, Deepak; Kumar, Harish: Entropy-stable schemes for relativistic hydrodynamics equations (2020)
  2. Ling, Dan; Duan, Junming; Tang, Huazhong: Physical-constraints-preserving Lagrangian finite volume schemes for one- and two-dimensional special relativistic hydrodynamics (2019)
  3. Chen, Yaping; Kuang, Yangyu; Tang, Huazhong: Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations (2017)
  4. Kidder, Lawrence E.; Field, Scott E.; Foucart, Francois; Schnetter, Erik; Teukolsky, Saul A.; Bohn, Andy; Deppe, Nils; Diener, Peter; Hébert, François; Lippuner, Jonas; Miller, Jonah; Ott, Christian D.; Scheel, Mark A.; Vincent, Trevor: SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics (2017)
  5. Qin, Tong; Shu, Chi-Wang; Yang, Yang: Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics (2016)
  6. Wu, Kailiang; Tang, Huazhong: High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics (2015)
  7. Wu, Kailiang; Tang, Huazhong: Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics (2014)
  8. Baeza, Antonio; Martínez-Gavara, Anna; Mulet, Pep: Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws (2012)
  9. Keppens, R.; Meliani, Z.; Van Marle, A. J.; Delmont, P.; Vlasis, A.; van der Holst, B.: Parallel, grid-adaptive approaches for relativistic hydro- and magnetohydrodynamics (2012)
  10. Yang, Zhicheng; Tang, Huazhong: A direct Eulerian GRP scheme for relativistic hydrodynamics: two-dimensional case (2012)
  11. Lee, T. S.; Zheng, J. G.; Winoto, S. H.: An interface-capturing method for resolving compressible two-fluid flows with general equation of state (2009)
  12. Van Der Holst, B.; Keppens, R.; Meliani, Z.: A multidimensional grid-adaptive relativistic magnetofluid code (2008)