CFDWARP — Computationally-Efficient Detailed Plasma Model  
CFDWARP is advantaged over other plasma aerodynamics codes through its novel computationally-efficient plasma model based on the drift-diffusion approximation. The drift-diffusion approximation is the commonly-used approach to simulate weakly-ionized plasmas at the macroscopic level. The drift-diffusion model consists of solving the charged species mass and momentum equations assuming that the forces due to inertia change are small compared to the collision forces, which is a valid assumption for many weakly-ionized plasmas. To close the system of equations, the electric field is determined by solving a potential equation obtained from Gauss's law.
While such a system of equations has had considerable success in simulating a wide range of problems including glow and dark discharge, ambipolar diffusion, ambipolar drift, etc, it suffers from high stiffness and very slow convergence whenever a quasi-neutral region forms (a quasi-neutral region is a region where the positive charge density is almost equal to the negative charge density). Because of this, the solution of weakly-ionized plasmas often requires hundreds of thousands and even millions of iterations to reach convergence. This leads to excessive computational efforts required to solve even the simplest cases.
In CFDWARP, an alternate strategy is used: instead of obtaining the potential equation from Gauss's law, the potential equation is obtained from Ohm's law and the ion transport equations are modified to ensure that Gauss's law is satisfied. As well, the electron transport equation is rewritten in ambipolar form to reduce its dependence on the potential. Recasting the system of equations in this manner relieves its stiffness substantially, and this results in a significant reduction of the number of iterations to reach convergence as well as an increase in resolution of the converged solution (a higher resolution here implies less grid-induced error on a given mesh). When combined together, these gains in convergence acceleration and resolution result in a one hundredfold increase in computational efficiency.
Such a recast of the drift-diffusion model is done without introducing simplifications: when the grid is refined sufficiently, the recast plasma equations used in CFDWARP yield the same solution as the conventional drift-diffusion equations (either in quasi-neutral regions or in non-neutral sheaths) despite requiring less than 1% of the computational effort.
Because of the novel recast alleviating the stiffness of the drift-diffusion model, it is possible to integrate the plasma transport equations in coupled form with the neutrals mass, momentum and energy conservation equations. This is in contrast to other plasma aerodynamics codes which solve the charged species equations and the neutrals transport equations using two different integration processes (which is necessary due to the conventional drift-diffusion model being too stiff to be integrated in coupled form with the neutrals). Using two different integration strategies does not only increase computational time but can also lead to problems in maintaining conservation or monotonicity when linking the two sets of equations together.
Such issues are avoided in our code where all transport equations are solved conjunctly, and advanced in time with a time step not considerably smaller than the one used to integrate non-ionized aerodynamic flows. This strategy results in CFDWARP exhibiting significantly faster convergence and higher resolution when solving plasma aerodynamics problems compared to other plasma codes.
The novel computationally-efficient plasma model used in CFDWARP was developed by our group in collaboration with Drs. Sergey Macheret and Mikhail Shneider of Princeton University and can be found in Refs. [4] and [5]. It is based on prior theory also developed by our group in Refs. [1,2,3]. How to implement the plasma model in a Navier-Stokes solver is outlined in Ref. [6].
[1]  B Parent, MN Shneider, SO Macheret. “Generalized Ohm's law and potential equation in computational weakly-ionized plasmadynamics”, Journal of Computational Physics, 230 (4), Pages 1439-1453, 2011.
[2]  B Parent, SO Macheret, MN Shneider. “Ambipolar diffusion and drift in computational weakly-ionized plasmadynamics”, Journal of Computational Physics, 230 (22), Pages 8010-8027, 2011.
[3]  B Parent, MN Shneider, SO Macheret. “Sheath Governing Equations in Computational Weakly-Ionized Plasmadynamics”, Journal of Computational Physics, 232 (1), Pages 234-251, 2013.
[4]  B Parent, SO Macheret, MN Shneider. “Electron and Ion Transport Equations in Computational Weakly-Ionized Plasmadynamics”, Journal of Computational Physics, 259, Pages 51-69, 2014.
[5]  B Parent, SO Macheret, MN Shneider. “Modeling Weakly-Ionized Plasmas in Magnetic Field: A New Computationally-Efficient Approach”, Journal of Computational Physics, 300, Pages 779-799, 2015.
[6]  B Parent, MN Shneider, SO Macheret. “Detailed Modeling of Plasmas for Computational Aerodynamics”, AIAA Journal, Article in Press, 2016.
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