Joel Thompson | University of Tennessee Space Institute (original) (raw)

Papers by Joel Thompson

43rd AIAA Plasmadynamics and Lasers Conference, 2012

A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is d... more A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is described. The approach implements a strongly conservative fluid formulation in which the Lorentz force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the Navier-Stokes equations, which have previously introduced severe stiffness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables the displacement current to be incorporated directly. To demonstrate the effectiveness of this technique, a fully explicit finite volume approximate Riemann solver is used to obtain numerical solutions to the Brio and Wu electromagnetic shock problem. Comparisons with the analytical solution show good agreement, and the implementation requires less than an hour of computational time on a single processor machine. Simulations using large and small conductivities confirm that the formulation captures both wave and diffusion limits of the magnetic field.

AIAA Journal, 2015

A solution procedure for the fully coupled Navier-Stokes and Maxwell equations is described. The ... more A solution procedure for the fully coupled Navier-Stokes and Maxwell equations is described. The approach implements a conservative fluid formulation in which the Lorentz body force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the fluid equations, which have previously introduced severe stiffness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables displacement current effects, charge separation effects, low-conductivity plasma behavior, and electromagnetic wave propagation to be incorporated directly. To circumvent the issue of complicated eigenvectors, an AUSM-type flux splitting scheme is proposed. Validation of the approach is presented for problems of electromagnetic wave propagation in low-conductivity plasma and high-conductivity magnetohydrodynamic problems, which demonstrates a robust, unified hyperbolic method for resolving both the wave and diffusion limits of the electromagnetic behavior in the plasma. Nomenclature A = area, m 2 a = speed of sound, m∕s B = magnetic induction field, T c 0 = speed of light in vacuum; 2.9979 × 10 8 m∕s E = electric field, V∕m e = internal energy ℱ = set of associated face elements F = flux vector F A = advective flux vector F C = coupling flux vector F P = pressure flux vector F A = upwinded advective flux vector F P = upwinded pressure flux vector H = total enthalpy H = source vector j = index of face element j c = electrical conduction current density, A∕m 2 k = index of volume element L = length scalê I = identity matrix M = Mach number M = face element Mach number n = index of iteration in pseudotime n = normal vector n e = electron number density, 1∕m 3 p = gas pressurê p = face element pressure Q = state vector q = heat flux vector, J∕m 3 q e = fundamental electronic charge; 1.6022 × 10 −19 C R = residual of volume element S EM = Poynting propagation vector, W∕m 2 t = Time, s U = solution vector u = velocity vector, m∕s V

50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2012

Plasma actuators have been extensively explored both experimentally and computationally. The elec... more Plasma actuators have been extensively explored both experimentally and computationally. The electromagnetic Lorentz body force and its appropriate modeling for design optimization has been the subject of some debate. The development of a superior model for this task has further been hampered by a limited understanding of the single dielectric barrier discharge physical process, particularly in the kinetics and chemical descriptions. Because of the wide range of applications the plasma actuator has already found, we expect future applications of the plasma actuator to require more advanced physical models including multiphysics simulations. This paper focuses on the development of a full Maxwell solver for the plasma actuator as an extension of a present Lorentz body force model. We aim to develop a tool for validation of different Lorentz force models and to provide a basis for multiphysics simulations of the plasma actuator.

44th AIAA Plasmadynamics and Lasers Conference, 2013

The AUSM family of schemes has been successful in simulating fluid dynamic and magnetohydrodynami... more The AUSM family of schemes has been successful in simulating fluid dynamic and magnetohydrodynamic flows. In this paper, we extend the AUSM method to solve the Navier-Stokes equations coupled to the full Maxwell equations. This approach permits the inclusion of electromagnetic wave propagation, displacement current and charge separation effects. Validation of the approach is presented for problems of electromagnetic wave propagation and magnetohydrodynamics, which demonstrates a robust, unified hyperbolic method for solving both the wave and diffusion limits in the same computational domain. . proach. We detail the construction of an AUSM-based (Advected Upstream Splitting Method) algorithm for solving a strong conservative formulation of the fluid equations without source terms, although exactly coupled to the full Maxwell equations. The new equations possess a very complicated eigenstructure. Previously, our efforts centered on developing a Roe approximate Riemann solver approach by first approximating the eigenstructure, 16 and then deriving the full eigenstructure; 17 however, as an alternative investigation, the AUSM family of schemes 18-21 was applied to the same equations, since this method does not require a knowledge of this eigenstructure, and provides an elegantly simple upwinded scheme for this complicated set of equations. We provide validation tests for electromagnetic wave propagation and magnetohydrodynamic tests to demonstrate the accuracy of the new approach.

Journal of Computational Physics, 2014

Please cite this article in press as: R.J. Thompson et al., A strong conservative Riemann solver ... more Please cite this article in press as: R.J. Thompson et al., A strong conservative Riemann solver for the solution of the coupled maxwell and Navier-Stokes equations, Journal of Computational Physics (2013), http://dx.

Physics of Plasmas, 2012

In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid eq... more In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic (MHD) limit restores the typical variety of MHD waves.

IEEE Transactions on Plasma Science, 2014

Recent efforts have extended fluid dynamic modeling to include low-electrical-conductivity (wavel... more Recent efforts have extended fluid dynamic modeling to include low-electrical-conductivity (wavelike) electromagnetic field effects in plasmas. Here, we present results of a new study to explore and illustrate the capability of resolving such effects in the development of plasma instabilities.

52nd Aerospace Sciences Meeting, 2014

An approximate Riemann solver approach is introduced for discretizing and solving the equations o... more An approximate Riemann solver approach is introduced for discretizing and solving the equations of relativistic two-fluid plasmadynamics. Such a general system of equations could permit physical investigations of plasmas where small-scale oscillations or inter-species effects could have long-term impact on the stability or overall behavior of a plasma. The solution procedure involves a pseudotime implicit scheme to discretize and solve the equations; the upwinded hydrodynamic and Maxwell fluxes are calculated separately by a Roe scheme, and the system is coupled through the presence of explicit source terms. Assessments of the solver's capabilities are provided by examining one-dimensional Riemann problem shock tube simulations.

IEEE Transactions on Plasma Science, 2000

Recent work has investigated the micro-laser ablation plasma thruster, a subkilogram form of sate... more Recent work has investigated the micro-laser ablation plasma thruster, a subkilogram form of satellite propulsion. Computational simulations that investigate the micro-thruster operation by the ablation of plasma through a nozzle using a magnetohydrodynamic code are presented. The performance improvement to the micro-thruster with a nozzle is compared to previous simulations wherein a passive solidpropellant was ablated without a nozzle. The model provides insight to the plasma generation and expansion from the fuel tape. Results show up to a 36% improvement in laser momentum coupling coefficient and up to 50% improvement in specific impulse.

51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2013

The effects of electromagnetic wave propagation, charge separation and higher-frequency effects c... more The effects of electromagnetic wave propagation, charge separation and higher-frequency effects can play a significant role in a plasma. Although the magnetohydrodynamic (MHD) model is the incumbent approach for describing plasmas of engineering interest, this model is incapable of resolving these features. In this paper, we introduce a split-flux Roe scheme approach for solving the single-fluid plasma model that retains the full Maxwell equations. This model is capable of resolving the missing effects. The approach is implemented in a multidimensional implicit dualtime solver and is validated against one-and two-dimensional problems of magnetohydrodynamics and electromagnetic wave propagation.

A new Riemann solver scheme for hyperbolic systems is introduced. The method consists of a discre... more A new Riemann solver scheme for hyperbolic systems is introduced. The method consists of a discretization of the initial data into an approximate representation by discrete, discontinuous waves. Instead of calculating an intercell flux based on these waves, the discontinuous waves are propagated directly. Since the sum total of all discontinuous waves represents an extension of the linear Riemann problem, the solution is determined straightforwardly. For nonlinear systems, each timestep is considered a separate linear Riemann problem, and the projected waves are weighted to a background grid. This method is strikingly similar to the particle-in-cell approach, except that discontinuous waves are pushed around instead of macroparticles. The method is applied to Maxwell's equations and the equations of inviscid gasdynamics. For linear systems, exact solutions can be achieved without dissipation, and exact transmissive boundary condition treatments are trivial to implement. For inviscid gasdynamics, the nonlinear method tended to resolve discontinuities more sharply than the Roe, HLL or HLLC methods while requiring only between 30% and 50% of the execution time under identical conditions. The approach is also extremely robust, as it works for any Courant number. In the limit that the Courant number becomes infinite, the nonlinear solution approaches the linearized solution.

A solution procedure for the fully coupled Navier–Stokes and Maxwell equations is described. The ... more A solution procedure for the fully coupled Navier–Stokes and Maxwell equations is described. The approach implements a conservative fluid formulation in which the Lorentz body force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the fluid equations, which have previously introduced severe stiffness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables displacement current effects, charge separation effects, low-conductivity plasma behavior, and electromagnetic wave propagation to be incorporated directly. To circumvent the issue of complicated eigenvectors, an AUSM-type flux splitting scheme is proposed. Validation of the approach is presented for problems of electromagnetic wave propagation in low-conductivity plasma and high-conductivity magnetohydrodynamic problems, which demonstrates a robust, unified hyperbolic method for resolving both the wave and diffusion limits of the electromagnetic behavior in the plasma.

Fluid dynamic plasma modeling has recently been extended to include the effects of weak coupling,... more Fluid dynamic plasma modeling has recently been extended to include the effects of weak coupling, where electromagnetic fields possess a wavelike nature, and charge separation effects, where quasi-neutrality may be violated. In this paper, we present a particular investigation of the MHD rotor problem to illustrate the successful capturing of both weakly coupled and strongly coupled (MHD) limits using the same numerical scheme.

Recent efforts have extended fluid dynamic modeling to include low-electrical conductivity (wavel... more Recent efforts have extended fluid dynamic modeling to include low-electrical conductivity (wavelike) electromagnetic field effects in plasmas. Here, we present results of a new study to explore and illustrate the capability of resolving such effects in the development of plasma instabilities.

Previous work recognized a new framework for the equations of a multifluid plasma, wherein each s... more Previous work recognized a new framework for the equations of a multifluid plasma, wherein each species can be described by a set of equations remarkably similar to the Maxwell equations of classical electrodynamics. This paper extends the previous effort to form an exact isomorphism between the multifluid theory and classical electrodynamics. The major benefits of the new formulation are that the explicit coupling between different species is minimized, and theorems and techniques of classical electrodynamics can be immediately applied to the new multifluid formulation. We introduce the exact isomorphism and investigate some of the immediate consequences from classical electrodynamics. To provide a visualization of the isomorphism, previous 1D and 2D numerical simulations are postprocessed and presented to illustrate the generalized fields and source terms.

Interest in development of micro- and nanosatellites has led to the design of the microlaser abla... more Interest in development of micro- and nanosatellites has led to the design of the microlaser ablation plasma thruster. Previous work succeeded in constructing a working computational model of the microthruster’s operation via MACH2, a two-dimensional magnetohydrodynamic code; however, this model was limited to simulating only nonenergetic solid propellant ablation in the microthruster. Recent experimental investigations have demonstrated that use of an exothermic (energetic) propellant can significantly improve performance of the microthruster and allow for higher-thrust modes of operation. The present work details new simulations of exothermic glycidyl azide subdetonation and full detonation processes; the results indicate a successful capability to match the detonation characteristics of the glycidyl azide and its ablative behavior. Particularly, the threshold for the onset of detonation in the fuel is explored and matches within approximately 14% of theoretical calculations of threshold pressure. This demonstrates the possibility to explore the selection of fuel for the microlaser ablation plasma thruster via computational investigations. Glycidyl azide polymer subdetonation simulations indicate a 74% improvement in impulse bit over the previous nonenergetic propellant. A confined ablation setup is also explored for detonation,
which demonstrates a vast improvement to performance while suppressing the propagation of shocks.

Recent work has investigated the microlaser ablation plasma thruster, which is a subkilogram form... more Recent work has investigated the microlaser ablation plasma thruster, which is a subkilogram form of satellite propulsion. Computational simulations that investigate the microthruster operation by the ablation of plasma through a nozzle using a magnetohydrodynamic code are presented. The performance improvement to the microthruster with a nozzle is compared with previous simulations wherein a passive solid propellant was ablated without a nozzle. The model provides insight to the plasma generation and expansion from the fuel tape. Results show up to a 36% improvement in the laser momentum coupling coefficient and up to 50% improvement in specific impulse.

Conference Presentations by Joel Thompson

43rd AIAA Plasmadynamics and Lasers Conference, 2012

AIAA Journal, 2015

50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2012

44th AIAA Plasmadynamics and Lasers Conference, 2013

Journal of Computational Physics, 2014

Physics of Plasmas, 2012

IEEE Transactions on Plasma Science, 2014

52nd Aerospace Sciences Meeting, 2014

IEEE Transactions on Plasma Science, 2000

51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2013

This paper details the development a unified hyperbolic model for fluid dynamics coupled to elect... more This paper details the development a unified hyperbolic model for fluid dynamics coupled to electromagnetics. The advantage to the model presented is that it includes the accurate physical behavior for several plasmas of aerospace interest; it can effectively capture both magnetohydrodynamic and electrohydrodynamic limits of the plasma, in addition to low-conductivity effects that expose the wave nature of the electromagnetic field. The approach is useful because of its potential for simplifying existing implementations towards multiphysics simulations of aerospace plasmas, eliminating the need for multiple implementations for different plasma models. In previous work, a Riemann solver approach and a flux-splitting approach have been introduced for this model. Here, we review their individual merits, present some assessment simulation results using both approaches, and compare them.

The AUSM family of schemes has been successful in simulating ﬂuid dynamic and magnetohydrodynamic... more The AUSM family of schemes has been successful in simulating ﬂuid dynamic and magnetohydrodynamic ﬂows. In this paper, we extend the AUSM method to solve the Navier-Stokes equations coupled to the full Maxwell equations. This approach permits the inclusion of electromagnetic wave propagation, displacement current and charge separation e ects. Validation of the approach is presented for problems of electromagnetic wave propagation and magnetohydrodynamics, which demonstrates a robust, uniﬁed hyperbolic method for solving both the wave and di usion limits in the same computational domain.

The effects of electromagnetic wave propagation, charge separation and higher-frequency effects c... more The effects of electromagnetic wave propagation, charge separation and higher-frequency effects can play a signiﬁcant role in a plasma. Although the magnetohydrodynamic (MHD) model is the incumbent approach for describing plasmas of engineering interest, this model is incapable of resolving these features. In this paper, we introduce a split-ﬂux Roe scheme approach for solving the single-ﬂuid plasma model that retains the full Maxwell equations. This model is capable of resolving the missing effects. The approach is implemented in a multidimensional implicit dualtime solver and is validated against one- and two-dimensional problems of magnetohydrodynamics and electromagnetic wave propagation.

A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is d... more A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is described. The approach implements a strongly conservative ﬂuid formulation in which the Lorentz force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the Navier-Stokes equations, which have previously introduced severe sti ness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables the displacement current to be incorporated directly. To demonstrate the e ectiveness of this technique, a fully explicit ﬁnite volume approximate Riemann solver is used to obtain numerical solutions to the Brio and Wu electromagnetic shock problem. Comparisons with the analytical solution show good agreement, and the implementation requires less than an hour of computational time on a single processor machine. Simulations using large and small conductivities conﬁrm that the formulation captures both wave and di usion limits of the magnetic ﬁeld.

This paper reviews a novel theoretical transformation of the two-fluid plasma equations into a se... more This paper reviews a novel theoretical transformation of the two-fluid plasma equations into a set of Maxwell’s equations, where new unified fields supplant the electric and magnetic fields, and contain both the fluid and electromagnetic character of the plasma. The challenge to using this framework is that a knowledge of the unified charge and unified current is presumed, which is a superposition of gasdynamic charge and current and electromagnetic charge and current. While electromagnetic charge and current are a familiar physical quantity, the idea of gasdynamic charge more foreign; therefore, this paper explores two numerical simulations where the unified charge and current is postprocessed and examined; this reveals some preliminary knowledge of the structure of the charge and current in the unified Maxwell equations.

Plasma actuators have been extensively explored both experimentally and computationally. The elec... more Plasma actuators have been extensively explored both experimentally and computationally. The electromagnetic Lorentz body force and its appropriate modeling for design optimization have been the subject of some debate. The development of a superior model for this task has further been hampered by a limited understanding of the single dielectric barrier discharge physical process, particularly in the kinetics and chemical descriptions. Because of the wide range of applications the plasma actuator has already found, we expect future applications of the plasma actuator to require more advanced physical models including multiphysics simulations. This paper focuses on the development of a full Maxwell solver for the plasma actuator as an extension of a present Lorentz body force model. We aim to develop a tool for validation of different Lorentz force models and to provide a basis for multiphysics simulations of the plasma actuator.

"An interest in the development of subkilogram forms of satellite micropropulsion has led to the ... more "An interest in the development of subkilogram forms of satellite micropropulsion has led to the design of the micro-laser plasma thruster (μLPT). Previous work succeeded in constructing a working computational model of the micro-thruster’s operation in the magnetohydrodynamic code MACH2; however, the previous work was limited to simulating only the non-energetic solid propellant ablation mode of the thruster. Recent experiments
have shown that the use of an exothermic propellant might be more beneficial for higher-thrust modes of operation. This work reviews improvements made to the computational model to simulate both the sub-detonation experimental ablation and laser-supported detonation of the glycidyl azide polymer fuel used in experiments. Simulation results indiciate that the sub-detonation ablation of this fuel demonstrates an improvement in the coupling
coefficient of 70% and in the specific impulse of 20% over the non-energetic solid-propellant case. The laser-supported detonation shows an increase in the coupling coefficient and specific impulse over the baseline solid-propellant case by at least two orders of magnitude.
The laser-supported detonation simulation also indicates vast damage to the fuel tape, but
the possibility of implementing rigid-wall boundary conditions to the fuel tape is presented.
"

Recent work has investigated the micro-laser ablation plasma thruster (μLPT), a sub-kilogram form... more Recent work has investigated the micro-laser ablation plasma thruster (μLPT), a sub-kilogram form of satellite propulsion. Computational simulations that simulate the operation of the micro-thruster using the magnetohydrodynamic code MACH2 have already been established. The investigations made here have extended the capabilities of the previous computational model and have been applied to a new micro-thruster operation design incorporating a conical nozzle to demonstrate enhanced thruster performance. A methodology is presented that was developed in the MACH2 code that allows for the calculation
of performance parameters characterizing the micro-thruster operation mode, such as coupling coefficient and specific impulse. The presence of a nozzle is shown to improve the
coupling coefficient by as much as 36% and the specific impulse by as much as 50%, and the resulting nozzle performance enhancement follows typical nozzle trends realized in thermal
rockets.