Parallelizaton of visual magneto-hydrodynamics code based on fluctuation distribution scheme on triangular grids

A two-dimensional (2D) magneto-hydrodynamics (MHD) code which has visualization and parallel processing capability is presented in this paper. The code utilizes a fluctuation splitting (FS) scheme that runs on structured or unstructured triangular meshes. First FS scheme which included the wave model: Model-A had been developed by Roe [Roe PL. Discrete models for the numerical analysis of time-dependent multi-dimensional gas dynamics. J Comp Phys 1986;63:458-76.] for the solutions of Euler's equations. The first 2D-MHD wave model: MHD-A, was then developed by Balci and Aslan [Balci Ş. The numerical solutions of two dimensional MHD equations by fluctuation splitting scheme on triangular meshes, Ph.D. Thesis, University of Marmara, Science-Art Faculty, Physics Dept Istanbul, Turkey; 2000; Aslan N. MHD-A: A fluctuation splitting wave model for planar magnetohydrodynamics. J Comp Phys 1999;153:437-66.] to solve MHD problems including shocks and discontinuities. It was then shown in [Balci S, Aslan N. Two dimensional MHD solver by fluctuation splitting and dual time stepping. Int J Numer Meth Fluids, in press.] that this code was capable of producing reliable results in compressible and nearly incompressible limits and under the effect of gravitational fields and that it was able to identically reduce to model-A of Roe in Euler limit with no sonic problems at rarefaction fans (Balci and Aslan, in press). An important feature of this code is its ability to run time dependent or steady problems on structured or unstructured triangular meshes that can be generated automatically by the code for specified domains. In order to use the parallel processing capability of the code, the triangular meshes are decomposed into different blocks in order to share the workload among a number of processors (here personal computers) which are connected by Ethernet. Due to the compact nature of the FS scheme, only one set of data transfer is required between neighbor processors. As it will be shown, this phenomenon results in minimum amount of communication loss and makes the scheme rather robust for parallel processing. The other important feature of the new code is its visual capability. As the code is running, colorful images of scalar quantities (density, pressure, Mach number, etc.) or vector graphics of vectoral quantities (velocity, magnetic field, etc.) can be followed on the screen. The extended code, called PV-MHDA, also allows following the trajectories of the particles in time by means of a recently included particle in cell (PIC) algorithm. Because the numerical dissipation embedded in its wave model reflects real physical viscosity and resistivity, it is able to run accurately for compressible flows (including shocks) as well as nearly incompressible flows (e.g., Kelvin-Helmholtz instability). The user-friendly visual and large-scale computation capability of the code allow the user more thorough analysis of MHD problems in two-dimensional complex domains. © 2006 Elsevier Ltd. All rights reserved. North Atlantic Treaty Organization Special thanks go to Ulvi Adalıoğlu (the director of Nuclear Engineering division of Cekmece Nuclear Research Center) for giving many valuable suggestions during the development of this code. Without his encourgements, combining parallel and visual versions of the code would be impossible. Good luck to him during his retirement. Partial support from NATO Collaborative Studies Programme is also acknowledged.