**6. References**


discharges dynamics and background gas dynamics. The experimental devices have to be very sensitive and precise in order to capture the main characteristics of nanosecond phenomena located in very thin filaments of micro scale extension. However, the recent evolution of experimental devices (ICCD or streak camera, DC and pulsed high voltage supply, among others) allow to better understand the physics of the micro-discharge. Furthermore, recent simulation of the micro-discharges involving the discharge and postdischarge phase in multidimensional dimension was found to give precise information about the chemical and hydrodynamics activation of the background gas in an atmospheric non-thermal plasma reactor. These kinds of simulation results, coupled with experimental investigation, can be used in future works for the development of new design of plasma reactor very well adapted to the studied application either in the environmental field or

All the simulations were performed using the HPC resources from CALMIP (Grant 2011-

Abahazem, A.; Merbahi, N.; Ducasse, O.; Eichwald, O. & Yousfi, M. (2008), Primary and

Bastien, F. & Marode, E. (1985), Breackdown simulation of electronegative gases in nonuniform field, *Journal of Physics D: Applied Physics*, Vol. 18, pp. 377-393 Batina, J.; Noel, F.; Lachaud, S. ; Peyrous, R. & Loiseau, J. F. (2001) Hydrodynamical

Bekstein, A.; Benhenni, M.; Yousfi, M.; Ducasse, O. & Eichwald, O. (2008), Ion swarm data of

Briels, T. M. P.; Kos J.; van Veldhuizen E. M. & Ebert, U. (2006), Circuit dependence of the

Byron, R.; Stewart, W. E.; Lightfoot E. N. (1960) Transport Phenomena, John Wiley & Sons Clement, F.; Held, B.; Soulem N. & Spyrou N. (2001). Polystyrene thin films treatment under

Dubois, D.; Merbahi, N.; Eichwald, O.; Yousfi, M.; Ducasse, O. & Benhenni, M. (2007),

mixtures, *Journal of Applied Physics*, Vol. 101, Issue 5, pp. 053304-053304-9 Dorai R. & Kushner M. (2003) Consequences of unburned hydrocarbons on microstreamer

discharges *Journal of Physics D: Applied Physics*,. Vol. 36, pp. 1075–1083 Eichwald, O.; Ducasse, O.; Merbahi, N.; Yousfi, M. & Dubois, D. (2006), Effect of order fluid

device, *Journal of Physics D: Applied Physics*, Vol. 34, pp. 1510–1524

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secondary streamer dynamics in pulsed positive corona discharges, *IEEE* 

simulation of the electric wind in a cylindrical vessel with positive point-to-plane

+ in N2, O2 , and dry air for streamer dynamics simulation , *European Physics* 

diameter of pulsed positive streamers in air, Journal of Physics D: Applied Physics,

DC pulsed discharges conditions in nitrogen, *The European Physical Journal, Applied* 

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dynamics and chemistry during plasma remediation of NO*x* using dielectric barrier

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[P1053] - www.calmip.cict.fr/spip/spip.php?rubrique90)

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biomedical one.

**6. References** 

N4

**5. Acknowledgment** 


**0**

**13**

*USA*

**An IMEX Method for the Euler Equations That**

**Posses Strong Non-Linear Heat Conduction and**

**Stiff Source Terms (Radiation Hydrodynamics)**

<sup>1</sup>*Idaho National Laboratory, Fuels Modeling and Simulation Department, Idaho Falls*

Here, we present a truly second order time accurate self-consistent IMEX (IMplicit/EXplicit) method for solving the Euler equations that posses strong nonlinear heat conduction and very stiff source terms (Radiation hydrodynamics). This study essentially summarizes our previous and current research related to this subject (Kadioglu & Knoll, 2010; 2011; Kadioglu, Knoll & Lowrie, 2010; Kadioglu, Knoll, Lowrie & Rauenzahn, 2010; Kadioglu et al., 2009; Kadioglu, Knoll, Sussman & Martineau, 2010). Implicit/Explicit (IMEX) time integration techniques are commonly used in science and engineering applications (Ascher et al., 1997; 1995; Bates et al., 2001; Kadioglu & Knoll, 2010; 2011; Kadioglu, Knoll, Lowrie & Rauenzahn, 2010; Kadioglu et al., 2009; Khan & Liu, 1994; Kim & Moin, 1985; Lowrie et al., 1999; Ruuth, 1995). These methods are particularly attractive when dealing with physical systems that consist of multiple physics (multi-physics problems such as coupling of neutron dynamics to thermal-hydrolic or to thermal-mechanics in reactors) or fluid dynamics problems that exhibit multiple time scales such as advection-diffusion, reaction-diffusion, or advection-diffusion-reaction problems. In general, governing equations for these kinds of systems consist of stiff and non-stiff terms. This poses numerical challenges in regards to time integrations, since most of the temporal numerical methods are designed specific for either stiff or non-stiff problems. Numerical methods that can handle both physical behaviors are often referred to as IMEX methods. A typical IMEX method isolates the stiff and non-stiff parts of the governing system and employs an explicit discretization strategy that solves the non-stiff part and an implicit technique that solves the stiff part of the problem. This standard IMEX approach can be summarized by considering a simple prototype model. Let us consider the following scalar

where *f*(*u*) and *g*(*u*) represent non-stiff and stiff terms respectively. Then the IMEX strategy

*<sup>u</sup>*<sup>∗</sup> <sup>−</sup> *<sup>u</sup><sup>n</sup>*

**1. Introduction**

model

Explicit block solves:

consists of the following algorithm blocks:

<sup>2</sup>*Los Alamos National Laboratory, Theoretical Division, Los Alamos*

Samet Y. Kadioglu<sup>1</sup> and Dana A. Knoll2

*ut* = *f*(*u*) + *g*(*u*), (1)

<sup>Δ</sup>*<sup>t</sup>* <sup>=</sup> *<sup>f</sup>*(*un*), (2)

