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Two-fluid Plasma Modelling
A substantial effort has been put into modelling plasma as coupled ion and electron fluids, each of which having separate motions and conserved quantities. Euler equations are advanced separately for each species, and the dynamics of their motions are coupled through the electromagnetic fields. The two-fluid description of plasma is more general than the more commonly used ideal or resistive MHD. Applications include modelling of the lower hybrid drift instabilities, collisionless magnetic reconnection, and stability of the field reversed configuration. More explanation of the project can be found here. This research is funded by the United States Air Force Office of Scientific Research. Multi-Dimensional Runge-Kutta Discontinuous Galerkin (RKDG) Method for Plasma Solvers
A solver based on the discontinuous Galerkin method is being developed. The discontinuous Galerkin method is a finite element scheme, which generalizes the finite volume wave propagation approach to arbitrary order of accuracy. One-dimensional comparisons have shown that the discontinuous Galerkin method is more robust in maintaining equilibrium than the currently used wave propagation method. It is also able to better resolve high frequency physical oscillations than the finite volume method. Recently, two dimensional simulations of collisionless magnetic reconnection, lower hybrid instabilities, and 2-dimensional Z-pinch have been successfully performed. The solver is currently being extended to include three spatial dimensions. A simulation for Euler equations of gas dynamics in 3D has been successfully performed, and an effort is made to couple the solver with elecromagnetic algorithms. Regions of Validity and Numerical Implementation of Ten Moment Two Fluid Plasma Modelling
A plasma model is derived by taking moments of the Boltzmann equation. With the inclusion of the update equations for the anisotropic pressure tensor, the ten moment system is able to resolve the finite Larmor radius effects. With the five-moment two fluid equations, the effects of collisions can be ignored because the plasma is assumed to be Maxwellian. However, the anisotropy of the pressure vanishes for a Maxwellian plasma. Therefore, to capture the anisotropic effect of the distribution function, the plasma is necessarily non-Maxwellian, which also implies that the effects of collisions and heat flux can no longer be ignored. Integrating effects of collisions as source terms of the ten moment system is the current research focus. The feasibility moment closure for heat flux is also currently investigated. Development of Divergence Error Free Electromagnetic Solvers for Two-Fluid Plasma Equations
A divergence error free electromagnetic solver for two-fluid plasma systems is developed. In three spatial dimensions, Maxwell's equations are a system of 8 equations and 6 unknowns, which, at first, may seem overdetermined. The two divergence equations are normally not included in the numerical calculation, because it has been analytically proven that, if the constraints are initially satisfied, they are mathematically satisfied for all times. However, numerical errors may arise, and these errors may lead to unphysical phenomena, such as numerical magnetic monopoles, and acceleration of plasma parallel to the field lines. To suppress the errors due to the violation of the divergence constraints, the Maxwell's equations are reformulated in terms of their potentials. 2nd order in time and space finite differencing is applied to solve the inhomogeneous wave equations for the scalar and the vector potentials. Successful benchmark applications include the GEM magnetic reconnection challenge, and a simulation of a steady state square wire carrying current. In both of these cases, the divergence error of the magnetic field is suppressed to machine truncation accuracy. The charge separation constraint, however, proves to be more difficult to satisfy. However, comparisons have been made, and the potential formulation satisfies the charge separation and solenoidality constraints better than the currently used perfectly hyperbolic Maxwell equations for two dimensional problems. Future work includes testing the shock capturing capability of the potential formulation, and also the sensitivity of the solutions due to the violations of the gauge conditions. WarpX
WarpX is a C++ framework, developed primarily for use of computational physics, taking advantage of multiple processor computer architecture by means of message passing interface. WarpX, written by Dr. Ammar Hakim, is currently being used and developed by the members of the Computational Fluid Dynamics Laboratory at the University of Washington, mainly for performing simulations of plasma physics. For more information regarding the software, please visit the WarpX wiki.
Principal Investigator
Lead Programmer
Graduate Research Assistants
- Robert Clifton Lilly
- Bhuvana Srinivasan - Andree Susanto |
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Send mail to: asbereth@u.washington.edu
Last modified: 5/02/2008 1:10 AM |
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