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Results for “compressible resistive MHD”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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10 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2020

Stable compression of a spherical tokamak plasma

In this study, an analysis of toroidal plasma compression by a collapsing flux conserver reveals linearly stable scenarios of operation to high compression ratios. The resistive and ideal MHD stability is calculated in full toroidal geometry using the asymptotic matching method in realistic conditions. A time dependent MHD simulation of the compression is conducted to confirm the conservation principles used to calculate the equilibrium states for the analysis. The near edge current profile, controlled by toroidal field ramping during compression, is shown to be critical to stability due to coupling between poloidal components of the least stable mode. Two cases with slight differences in edge current are examined, one with a stable corridor to high compression and one without.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A stable corridor for toroidal plasma compression

In this study, a toroidal plasma compressed by a collapsing flux conserver is analyzed to reveal stable scenarios of operation to high compression ratios. The resistive and ideal MHD stability is calculated in full toroidal geometry, using the asymptotic matching method in realistic conditions, and comparing with nonlinear simulations. The near edge current profile, controlled by toroidal field ramping during compression, is shown to be critical to stability due to coupling between poloidal components of the least stable mode. The extension of a length of shaft on axis is also found to be critical at high compression, as the resulting good curvature region in magnetic field stabilizes pressure driven modes that would otherwise be unstable. This work extends from previous studies, which initially showed the existence of a stable scenario, to include findings of more extensive stable zones, detailed effects of geometry, and nonlinear simulations of the instabilities. The nonlinear simulations of the compression are consistent with the linear analyses, confirming both the conservation and stability properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Deep Koopman Neural Network for Analyzing High-Energy-Density Simulations of Electrical Wire Explosions

Megaampere-scale electrical wire experiments (EWEs) provide a platform for studying magnetohydrodynamic (MHD) instability growth in magneto-inertial fusion (MIF) devices. Even when nonlinear simulations of these experiments can digitally reproduce much of the experimentally observed instability growth, interpreting the results and understanding mode growth and evolution can be non-trivial. As a first step toward providing better interpretation of these simulation features, this work investigates the use of a deep neural network that uses Koopman operator theory to analyze the dynamics of pulsed-power-driven explosions of EWEs. This deep neural network is trained on 1-D resistive MHD simulations of EWEs. This neural network learns to transform the nonlinear data into a lower-dimensional representation where the time dynamics are linear. Layers of this neural network are shown to learn features of the simulations, including the locations of shock waves and different physical regimes of the simulation. Using the learned features, the network can compress a time state of the simulation consisting of 5120 data point into a 36-parameter lower-dimensional latent space embedding. Furthermore, these embeddings are shown to be clustered in the latent space by initial radius and time state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simulating a pulsed-power-driven plasma with ideal MHD

We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representation is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Kelvin–Helmholtz instability under stabilizing parallel magnetic field in nonhomogeneous compressible MHD flows

We study the Kelvin–Helmholtz instability (KHI) for the general case of a compressible, nonhomogeneous, magnetized plasma flow. The study is limited to a vortex sheet interface with an imposed parallel magnetic field. We introduce a new formalism based on a convective Mach number M c , a convective Alfvénic Mach number M Ac , and a total convective Mach number that combines the two. We derive an analytic expression of the KHI growth rate for a homogeneous flow (i.e., zero Atwood number, A=0) that converges toward both the expression for unmagnetized compressible flow and Chandrasekhar's expression for magnetized incompressible flow. Otherwise, the dispersion relation is solved numerically and allows deriving general stability diagrams of magnetized KHI for the triplet (A, M c , β −plasma) parameters. We show these parameters uniquely define all configurations for a parallel magnetic field. We also construct diagrams with respect to the convective Alfvénic Mach number, the β − plasma parameter, or the magnetic field showing which magnetic field strength is required for stabilizing a given shear flow. The theoretical growth rates are compared with 18 simulations made with the GAMERA code, currently used for 3D magnetospheric simulations. Finally, we apply our results to the analysis of a past KHI experiment performed at the OMEGA laser facility, showing linear theory succeeds to provide accurate estimates of the growth rate at early times. We further discuss how our results can inform future experiments in the high-Mach magnetized regime at the National Ignition Facility. Possible limitations of the study due to resistive, mixing, or turbulence effects are discussed.

compressible flows↗
DOE OSTI2025

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium (ISM), which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu _{\text{bulk}}$, deriving a new $\nu _{\text{bulk}}$ Reynolds number $\text{Re}_{\text{bulk}}$, and viscous Prandtl number $\text{P}\nu \equiv \text{Re}_{\text{bulk}}/ \text{Re}_{\text{shear}}$, where $\text{Re}_{\text{shear}}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\boldsymbol {\nabla }\otimes \mathrm{{\boldsymbol {\mathit {v}}}}$, where $\mathrm{{\boldsymbol {\mathit {v}}}}$ is the fluid velocity. We find that $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $\nu _{\text{bulk}}$ ($\text{P}\nu \rightarrow \infty$), $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\text{P}\nu \approx 1$. As $\text{P}\nu$ decreases, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ are dissipated at increasingly larger scales, in turn suppressing incompressible modes through a coupling between high-k modes. We emphasize the importance of further understanding the role of $\nu _{\text{bulk}}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

MHD↗