Ravi Samtaney

Formation of Plasmoid Chains in Magnetic Reconnection

A detailed numerical study of magnetic reconnection in resistive MHD for very large, previously inaccessible, Lundquist numbers (10(4) <or= S <or= 10(8)) is reported. Large-aspect-ratio Sweet-Parker current sheets are shown to be unstable to super-Alfvénically fast formation of plasmoid (magnetic-island) chains. The plasmoid number scales as S(3/8) and the instability growth rate in the linear stage as S(1/4), in agreement with the theory by Loureiro et al. [Phys. Plasmas 14, 100703 (2007)]. In the nonlinear regime, plasmoids continue to grow faster than they are ejected and completely disrupt the reconnection layer. These results suggest that high-Lundquist-number reconnection is inherently time-dependent and hence call for a substantial revision of the standard Sweet-Parker quasistationary picture for S>10(4).

Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas

A numerical study of magnetic reconnection in the large-Lundquist-number (S), plasmoid-dominated regime is carried out for S up to 107. The theoretical model of Uzdensky et al. [Phys. Rev. Lett. 105, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is Eeff∼0.02 independently of S for S≫104. The plasmoid flux (Ψ) and half-width (wx) distribution functions scale as f(Ψ)∼Ψ-2 and f(wx)∼wx-2. The joint distribution of Ψ and wx shows that plasmoids populate a triangular region wx≳Ψ/B0, where B0 is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic “monster” plasmoids with wx∼10% of the system size are shown to emerge in just a few Alfven times, independently of S, suggesting that large disruptive events are an inevitable feature of large-S reconnection.

A Virtual Test Facility for the Simulation of Dynamic Response in Materials

The Center for Simulating Dynamic Response of Materials at the California Institute of Technology is constructing a virtual shock physics facility for studying the response of various target materials to very strong shocks. The Virtual Test Facility (VTF) is an end-to-end, fully three-dimensional simulation of the detonation of high explosives (HE), shock wave propagation, solid material response to pressure loading, and compressible turbulence. The VTF largely consists of a parallel fluid solver and a parallel solid mechanics package that are coupled together by the exchange of boundary data. The Eulerian fluid code and Lagrangian solid mechanics model interact via a novel approach based on level sets. The two main computational packages are integrated through the use of Pyre, a problem solving environment written in the Python scripting language. Pyre allows application developers to interchange various computational models and solver packages without recompiling code, and it provides standardized access to several data visualization engines and data input mechanisms. In this paper, we outline the main components of the VTF, discuss their integration via Pyre, and describe some recent accomplishments in large-scale simulation using the VTF.

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 10243, 20483, and 40963 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.

Regular shock refraction at an oblique planar density interface in magnetohydrodynamics

We consider the problem of regular refraction (where regular implies all waves meet at a single point) of a shock at an oblique planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic (MHD) simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180 ◦ rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the types of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180 ◦ rotational discontinuities, each followed by a slowmode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading-order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively.

An adaptive mesh semi-implicit conservative unsplit method for resistive MHD

We present a cell-centered semi-implicit algorithm for solving the equations of single fluid resistive MHD for block structured adaptive meshes. The unsplit method [1] is extended for the ideal MHD part, and the diffusive terms are solved implicitly. The resulting second-order accurate scheme is conservative while preserving the ∇ · B = 0 constraint. Numerical results from a variety of verification tests are presented.

The Richtmyer–Meshkov instability in magnetohydrodynamics

The Richtmyer-Meshkov instability is important in applications including inertial confinement fusion and astrophysical phenomena. In some applications, the fluids involved are plasmas and can be affected by magnetic fields. For one configuration, it has been numerically demonstrated that the growth of the instability is suppressed in the presence of a magnetic field. Here, the nature of this suppression is theoretically and numerically investigated. In ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated perturbed density interface in the presence of a magnetic field initially parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the magnetic field, but the interface amplitude then asymptotes to a constant value. Thus the instability is suppressed. The interface behavior from the model is compared to the results of compressible simulations. We then consider regular shock refraction at an oblique planar density interface in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic simulations indicate that the presence of the magnetic field inhibits the deposition of vorticity on the shocked contact, which leads to the suppression of the Richtmyer-Meshkov instability. We show that the shock refraction process produces a system of five to seven plane waves that intersect at a point. In all solutions, the shocked contact is vorticity free. These solutions are not unique, but differ in the type of waves that participate. The equations governing the structure of these multiple-wave solutions are obtained and a numerical method of solution is described. Solutions are compared to the results of simulations. The limit of vanishing magnetic field is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular wedge whose angle scales with the applied field magnitude. The shock-induced shear across the wedge is supported by slow-mode expansion fans within it, leaving the shocked contact vorticity free. To verify these findings, an approximate leading order asymptotic solution was computed.

3D adaptive mesh refinement simulations of pellet injection in tokamaks

We present results of Adaptive Mesh Refinement (AMR) simulations of the pellet injection process, a proven method of refueling tokamaks. AMR is a computationally efficient way to provide the resolution required to simulate realistic pellet sizes relative to device dimensions. The mathematical model comprises of single-fluid MHD equations with source terms in the continuity equation along with a pellet ablation rate model. The numerical method developed is an explicit unsplit upwinding treatment of the 8-wave formulation, coupled with a MAC projection method to enforce the solenoidal property of the magnetic field. The Chombo framework is used for AMR. The role of the E x B drift in mass redistribution during inside and outside pellet injections is emphasized.

A direct numerical simulation investigation of the synthetic jet frequency effects on separation control of low-Re flow past an airfoil

We present results of direct numerical simulations of a synthetic jet (SJ) based separation control of flow past a NACA-0018 (National Advisory Committee for Aeronautics) airfoil, at 10° angle of attack and Reynolds number 104 based on the airfoil chord length C and uniform inflow velocity U0. The actuator of the SJ is modeled as a spanwise slot on the airfoil leeward surface and is placed just upstream of the leading edge separation position of the uncontrolled flow. The momentum coefficient of the SJ is chosen at a small value 2.13 × 10−4 normalized by that of the inflow. Three forcing frequencies are chosen for the present investigation: the low frequency (LF) F+ = feC/U0 = 0.5, the medium frequency (MF) F+ = 1.0, and the high frequency (HF) F+ = 4.0. We quantify the effects of forcing frequency for each case on the separation control and related vortex dynamics patterns. The simulations are performed using an energy conservative fourth-order parallel code. Numerical results reveal that the geometric v...

The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers.