Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH

Murawski, K.; Lee, D.

doi:10.2478/v10175-011-0012-3

Cited by 9 publications

(10 citation statements)

References 34 publications

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“…Murawski and Lee, 2012) are one of several numerical techniques available to solve the MHD equations, (e.g. Murawski and Lee, 2011). These methods are simple to implement, easily adaptable to complex geometries, and well suited to handle nonlinear terms.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

Murawski

Ballai

Srivastava

et al. 2013

Monthly Notices of the Royal Astronomical Society

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With the adaptation of the FLASH code we simulate magnetohydrodynamic-gravity waves and vortices as well as their response in the magnetized three-dimensional (3D) solar atmosphere at different heights to understand the localized energy transport processes. In the solar atmosphere strongly structured by gravitational and magnetic forces, we launch a localized velocity pulse (in horizontal and vertical components) within a bottom layer of 3D solar atmosphere modeled by initial VAL-IIIC conditions, which triggers waves and vortices. The rotation direction of vortices depends on the orientation of an initial perturbation. The vertical driver generates magnetoacousticgravity waves which result in oscillations of the transition region, and it leads to the eddies with their symmetry axis oriented vertically. The horizontal pulse excites all magnetohydrodynamic-gravity waves and horizontally oriented eddies. These waves propagate upwards, penetrate the transition region, and enter the solar corona. In the high-beta plasma regions the magnetic field lines move with the plasma and the temporal evolution show that they swirl with eddies. We estimate the energy fluxes carried out by the waves in the magnetized solar atmosphere and conclude that such wave dynamics and vortices may be significant in transporting the energy to sufficiently balance the energy losses in the localized corona. Moreover, the structure of the transition region highly affects such energy transports, and causes the channeling of the propagating waves into the inner corona.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

Murawski

Ballai

Srivastava

et al. 2013

Monthly Notices of the Royal Astronomical Society

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“…The numerical simulations in this paper are performed with the use of the newly developed adaptive mesh refinement GAMER code [3,4], which implements a second-order unsplit Godunov solver [5][6][7].…”

Section: Numerical Simulations With the Gamer Codementioning

confidence: 99%

Numerical simulations of acoustic waves with the graphic acceleration GAMER code

Murawski¹,

Schive²

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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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.

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“…This method was proved to be stable by Berthon [8,9] and it was used in a number of applications, see for instance [10,11], and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…The reason we pay our attention on this method is its robustness and accurate representation of complex solutions [10,11]. We realize our aim by reviewing theory of the Euler equations in the following section.…”

Section: Introductionmentioning

confidence: 99%

Implementation of MUSCL-Hancock method into the C++ code for the Euler equations

Murawski¹,

Stpiczyński²

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. In this paper we present implementation of the MUSCL-Hancock method for numerical solutions of the Euler equations. As a result of the internal complexity of these equations solving them numerically is a formidable task. With the use of the original C++ code, we developed and presented results of a numerical test that was performed. This test shows that our code copes very well with this task.

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Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH

Cited by 9 publications

References 34 publications

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

Numerical simulations of acoustic waves with the graphic acceleration GAMER code

Implementation of MUSCL-Hancock method into the C++ code for the Euler equations

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