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K. Murawski

Numerical solutions of magnetohydrodynamic equations

In this paper we review several mathematical aspects in numerical methods for magnetohydrodynamic equations. The intrinsic complexity and the requirements of the selenoidity condition make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system, which reveal that the numerical methods cope very well with this task.

Open access

K. Murawski, K. Murawski and P. Stpiczyński

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

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.

Open access

K. Murawski and D. Lee

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

In this paper we review numerical methods for hydrodynamic equations. Internal complexity make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system with a use of a publicly available code, FLASH. These results proof that the numerical methods cope very well with this task.

Open access

K. Murawski and T. Tanaka

Abstract.

This paper is concerned with a numerical solutions of two-component magnetohydrodynamic equations. While a hyperbolic system of wave equations admits a shock solution as a result of the selenoidality condition the MHD equations are not strictly hyperbolic. As a consequence of that these equations require special numerical treatment. An application of a resulting numerical code to a problem of solar wind interaction with the ionosphere of the planet Venus is presented.

Open access

Krzysztof Murawski

Abstract

The paper presents the construction and operation of a video sensor developed for video-manometer. In the publication the use of video-manometer for measuring gas pressure is presented. A characteristic feature of the device is pressure measurement based on diaphragm deformation and digital image processing. Presented measuring technique eliminates restrictions in the construction of the measuring apparatus arising from non-linear nature of diaphragm deformation. It also allows performing measurements of gas pressure, also of explosive gas, providing galvanic isolation between the factor measured and the measuring device. The paper presents the results of video-manometer calibration and measurements taken during the laboratory tests. It has been shown that the developed video-manometer, that is equipped with a flat silicone diaphragm, allows measuring the gas pressure in the range of 0 – 100 mbar with an error less than 2 %. In the experiments the CO2 pressure was measured.

Open access

K. Murawski, K. Murawski and H.-Y. Schive

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.

Open access

A. Wasiljew and K. Murawski

Abstract

We present a new version of the Athena code, which solves magnetohydrodynamic equations in two-dimensional space. This new implementation, which we have named Athena-GPU, uses CUDA architecture to allow the code execution on Graphical Processor Unit (GPU). The Athena-GPU code is an unofficial, modified version of the Athena code which was originally designed for Central Processor Unit (CPU) architecture.

We perform numerical tests based on the original Athena-CPU code and its GPU counterpart to make a performance analysis, which includes execution time, precision differences and accuracy. We narrowed our tests and analysis only to double precision floating point operations and two-dimensional test cases. Our comparison shows that results are similar for both two versions of the code, which confirms correctness of our CUDA-based implementation. Our tests reveal that the Athena-GPU code can be 2 to 15-times faster than the Athena-CPU code, depending on test cases, the size of a problem and hardware configuration.