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MACH3: A CHSSI code for computational magnetohydrodynamics of general materials in generalized coordinates
Abstract
We were funded via the Common HPC Software Support Initiative (CHSSI) from 2000-2002 to develop a fully 3D arbitrary-coordinate parallel time-domain magnetohydrodynamic (MHD) simulation code - the CEA-10 project. CEA-10 built upon the single-fluid MHD, arbitrary Lagrangian-Eulerian multiblock, multitemperature, simulation environment called MACH3 (Multibloch Arbitrary Coordinate Hydromagnetics in 3D). The CEA-10 software underwent successful beta testing and review in December 2002. The beta tests consisted of five simulations: 1D magnetic diffusion, 2D Alfvenic shock, 2D flow over a wedge, 3D gas-filled rod pinch, and 3D laser-target interactions, run on various HPC platforms. The first three have analytic solutions and last two have experimental data and qualitative models to which simulated results can be compared. We obtained different scaled efficiency and parallel speedup results on different platforms and for different test problems.
... Elastic-plastic hydrodynamic simulation is an effective approach to investigate numerically important physical questions of materials under high-pressure ramp wave loading, such as structure phase transition, yield intensity, constitutive relations, and chemical reaction, as well as the effects of strain rate and temperature [29]- [32]. As many advanced hydrocodes [33]- [35], the code SSS [36] can conduct elasticplastic-reactive hydrodynamic calculations, in which the word reactive means a hydrodynamic model of two components representing detonation products and unreacted explosive, respectively. Detonation reaction and propagation can be described with the transition process of the two components. ...
Based on the 1-D elastic-plastic reactive hydrodynamic code Simplified Stretch Sin, a magnetohydrodynamic (MHD) version SSS/MHD has been developed. The new code is of multifield coupling, making use of the Resistance-Inductance-Capacitance circuit equations related to loading currents and others. To calculate MHD and circuit variables consistently and simultaneously, on the basis of Faraday's law, the relations between loading currents and magnetic flux in configuration cavities, variation in total magnetic flux and back electromotive force, and an iteration procedure are employed. The sample configurations in magnetically driven isentropic compression experiments (ICEs) here consist of parallel slabs and cavities, in which the step targets are a pair of slabs symmetrical to loading electrodes and of the same sample material but different in thickness. Self-consistent MHD and circuit calculations for ICE step targets of aluminum, tantalum, and plastic binder explosive is reported in this paper. The results agree with the measured ones well, including loading current profiles and velocity histories on samples' free surface or optics window interface. Since the input data for this code are geometric sizes, material parameters, and original circuit parameters only, its results are independent of measured or empirical data, and could be helpful in design and prediction of ICE or other experiments.
A numerical model employing the ablation rate and ionization of Teflon is developed to analyze pulsed plasma thruster (PPT) performance. A one-dimensional lumped circuit analysis model is implemented to calculate the discharge current. The Saha equation and Keidar Teflon ablation model are used to analyze the ionization of carbon and fluorine molecules produced by the Teflon gas. The numerical model also predicts the electron temperature distribution and simplified plasma shape during the discharge. Numerical simulation results with different voltage conditions compare reasonably well with experimental data. The Teflon gas flux reaches its maximum value at the maximum electron temperature and then gradually decays. The multivalent ions are investigated for PPT operation.
A plasma-filled rod-pinch diode, fielded on the NRL Gamble II generator, may represent a breakthrough in concentrating electron-beam energy into a small volume. Injected plasma connects the grounded cathode to the concentric tungsten rod anode. After a short-circuit phase lasting 10-30 ns, the impedance increases and a large fraction of the electron-beam energy is deposited on the tip of the rod, producing a small, intense X-ray source. As the injected plasma density increases, the current and voltage (at the time of maximum radiation) range from 260 kA and 1.8 MV to 770 kA and 0.45 MV. These parameters imply effective anode-cathode gaps of 130 to 7 μm, far smaller than can be achieved with metal electrodes without premature shorting. The physics of the plasma-filled rod-pinch diode differs from its vacuum analog. Current can be convected to the rod tip by plasma translation instead of electron-beam propagation. When plasma is pushed beyond the tip of the rod, a gap can form there by erosion. The high current and voltage, combined with the small anode diameter, may produce record electron-beam power densities (75 TW/cm2) and high-energy-density plasma conditions at the rod tip. Potential applications include improved radiography sources, X-ray/matter interaction studies, and high-energy-density plasma generation.
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We have developed a multiblock arbitrary coordinate Hydromagnetics (MACH) code for computing the time-evolution of materials of arbitrary phase (solid, liquid, gas, and plasma) in response to forces that arise from material and magnetic pressures. MACH is a single-fluid, time-dependent, arbitrary Lagrangian-Eulerian (ALE) magnetohydrodynamic (MHD) simulation environment. The 2 1/2 -dimensional MACH2 and the parallel 3-D MACH3 are widely used in the MHD community to perform accurate simulation of the time evolution of electrically conducting materials in a wide variety of laboratory situations. In this presentation, we discuss simulations of the interaction of an intense laser beam with a solid target in an ambient gas. Of particular interest to us is a laser-supported detonation wave (blast wave) that originates near the surface of the target when the laser intensity is sufficiently large to vaporize target material within the focal spot of the beam. Because the MACH3 simulations are fully three-dimensional, we are able to simulate non-normal laser incidence. A magnetic field is also produced from plasma energy near the edge of the focal spot.
1. Introduction.- 2. Single-Particle Motions.- 3. Plasmas as Fluids.- 4. Waves in Plasmas.- 5. Diffusion and Resistivity.- 6. Equilibrium and Stability.- 7. Kinetic Theory.- 8. Nonlinear Effects.- Appendices.- Appendix A. Units, Constants and Formulas, Vector Relations.- Appendix B. Theory of Waves in a Cold Uniform Plasma.- Appendix C. Sample Three-Hour Final Exam.- Appendix D. Answers to Some Problems.- Index to Problems.
Numerical corrections are made to previous values for the power absorption coefficient and some common errors noted.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Photographs by J. E. Mack of the first atomic explosion in New Mexico were measured, and the radius, R, of the luminous globe or 'ball of fire' which spread out from the centre was determined for a large range of values of t, the time measured from the start of the explosion. The relationship predicted in part I, namely, that R5/2 would be proportional to t, is surprisingly accurately verified over a range from R=20 to 185 m. The value of R5/2t-1 so found was used in conjunction with the formulae of part I to estimate the energy E which was generated in the explosion. The amount of this estimate depends on what value is assumed for gamma , the ratio of the specific heats of air. Two estimates are given in terms of the number of tons of the chemical explosive T.N.T. which would release the same energy. The first is probably the more accurate and is 16,800 tons. The second, which is 23,700 tons, probably overestimates the energy, but is included to show the amount of error which might be expected if the effect of radiation were neglected and that of high temperature on the specific heat of air were taken into account. Reasons are given for believing that these two effects neutralize one another. After the explosion a hemispherical volume of very hot gas is left behind and Mack's photographs were used to measure the velocity of rise of the glowing centre of the heated volume. This velocity was found to be 35 m./sec. Until the hot air suffers turbulent mixing with the surrounding cold air it may be expected to rise like a large bubble in water. The radius of the 'equivalent bubble' is calculated and found to be 293 m. The vertical velocity of a bubble of this radius is 2/3\ surd (g29300) or 35\cdot 7 m./sec. The agreement with the measured value, 35 m./sec., is better than the nature of the measurements permits one to expect.
We illustrate a new technique for computing the time-evolution of magnetic flux on a generally nonorthogonal computational grid of a time-dependent, arbitrary Lagrangian–Eulerian magnetohydrodynamics (MHD) simulation code and apply this technique to some classical MHD test problems. For a nontrivial application, we demonstrate the power of this technique for the interesting problem of compact toroid translation between a pair of converging conical electrodes.
Recently, upwind differencing schemes have become very popular for solving hyperbolic partial differential equations, especially when discontinuities exist in the solutions. Among many upwind schemes successfully applied to the problems in gas dynamics, Roe's method stands out for its relative simplicity and clarity of the underlying physical model. In this paper, an upwind differencing scheme of Roe-type for the MHD equations is constructed. In each computational cell, the problem is first linearized around some averaged state which preserves the flux differences. Then the solution is advanced in time by computing the wave contributions to the flux at the cell interfaces. One crucial task of the linearization procedure is the construction of a Roe matrix. For the special case γ = 2, a Roe matrix in the form of a mean value Jacobian is found, and for the general case, a simple averaging procedure is introduced. All other necessary ingredients of the construction, which include eigenvalues, and a complete set of right eigenvectors of the Roe matrix and decomposition coefficients are presented. As a numerical example, we chose a coplanar MHD Riemann problem. The problem is solved by the newly constructed second-order upwind scheme as well as by the Lax-Friedrichs, the Lax-Wendroff, and the flux-corrected transport schemes. The results demonstrate several advantages of the upwind scheme. In this paper, we also show that the MHD equations are nonconvex. This is a contrast to the general belief that the fast and slow waves are like sound waves in the Euler equations. As a consequence, the wave structure becomes more complicated; for example, compound waves consisting of a shock and attached to it a rarefaction wave of the same family can exist in MHD.