Numerical simulations of acoustic waves with the graphic acceleration GAMER code

Open access

Abstract

We present results of numerical simulations of acoustic waves with the use of the Graphics Processing Unit (GPU) acceleration GAMER code which implements a second-order Godunov-type numerical scheme and adaptive mesh refinement (AMR). The AMR implementation is based on constructing a hierarchy of grid patches with an octree data structure. In this code a hybrid model is adopted, in which the time-consuming solvers are dealt with GPUs and the complex AMR data structure is manipulated by Central Processing Units (CPUs). The code is highly parallelized with the Hilbert space-filling curve method. These implementations allow us to resolve well desperate spatial scales that are associated with acoustic waves. We show that a localized velocity (gas pressure) pulse that is initially launched within a uniform and still medium triggers acoustic waves simultaneously with a vortex (an entropy mode). In a flowing medium, acoustic waves experience amplitude growth or decay, a scenario which depends on a location of the flow and relative direction of wave propagation. The amplitude growth results from instabilities which are associated with negative energy waves.

[1] NVIDIA, NVIDIA CUDA C Programming Guide (Version 4.1), Santa Clara, CA, NVIDIA, 2012.

[2] Khronos Group, The OpenCL Specification (Version 1.2), Beaverton, OR, Khronos Group, 2011.

[3] H. Schive, Y. Tsai, and T. Chiueh, “GAMER: a graphic processing unit accelerated adaptive-mesh-refinement code for astrophysics”, Astrophys. J. Suppl. 186, 457-484 (2010).[4] H. Schive, U. Zhang, and T. Chiueh, “Directionally unsplit hydrodynamic schemes with hybrid MPI/OpenMP/GPU parallelization in AMR”, CD-ROM arXiv 1103.3373(2011).

[5] S.K. Godunov, “A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations”, Math. Sb. 47, 271-306, (1959).

[6] K. Murawski Jr., K. Murawski, and P. Stpiczyński, “Implementation of MUSCL-Hancock method into the C++ code for the Euler equations”, Bull. Pol. Ac.: Tech. 60 (1), 45-53 (2012).

[7] K. Murawski, D. Lee, “Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH”, Bull. Pol. Ac.: Tech. 59 (1), 81-91 (2011).

[8] J. Lighthill, Waves in Fluids, Cambridge University Press, Cambridge, 1978.

[9] D.J. Acheson, Elementary Fluid Dynamics, Oxford University Press, New York, 1990.

[10] K. Murawski, T.V. Zaqarashvili, and V.M. Nakariakov, “Entropy mode at a magnetic null point as a possible tool for indirect observation of nanoflares in the solar corona”, Astron. Astrophys. 533, A18 1-5 (2011).

[11] R.A. Cairns, “The role of negative energy waves in some instabilities of parallel flows”, J. Fluid Mech. 92, 1-14 (1979).

[12] M. Terra-Homem, R. Erdelyi, and I. Ballai, “Linear and nonlinear MHD wave propagation in steady-state magnetic cylinders”, Solar Physics 217, 199-223 (2003).

[13] P.S. Joarder, V.M. Nakariakov, and B. Roberts, “A manifestation of negative energy waves in the solar atmosphere”, SolarPhysics 176, 285-297 (1997).

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 103 102 6
PDF Downloads 32 31 5