Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T09:24:37.784Z Has data issue: false hasContentIssue false
  • English
  • Français

A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases

Published online by Cambridge University Press:  03 June 2015

Chijie Zhuang  and
Rong Zeng
Chijie Zhuang
Affiliation:
State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
Rong Zeng*
Affiliation:
State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
*
Email:[email protected]
Get access

Abstract

Assumed having axial symmetry, the streamer discharge is often described by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson’s equation. Without additional care for a stricter CFL condition or special treatment to the negative source term, popular methods used in streamer discharge simulations, e.g., FEM-FCT, FVM, cannot ensure the positivity of the particle densities for the cases in attaching gases. By introducing the positivity-preserving limiter proposed by Zhang and Shu [15] and Strang operator splitting, this paper proposes a finite difference scheme with a provable positivity-preserving property in cylindrical coordinate system, for the numerical simulation of streamer discharges in non-attaching and attaching gases. Numerical examples in non-attaching gas (N2) and attaching gas (SF6) are given to illustrate the effectiveness of the scheme.

Keywords

65Z0565M0668U20WENO finite differencepositivity-preservingstreamer dischargenumerical simulation
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 1 , January 2014 , pp. 153 - 178
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ebert, U., Nijdam, S., Li, C., et al. Review of recent results on streamer discharges and their relevance for sprites and lightning. Journal of Geophysical Research, 2010, 115(A2): A00E43.Google Scholar
[2] Montijn, C., Hundsdorfer, W. and Ebert, U. An adaptive grid refinement strategy for the simulation of negative streamers. Journal of Computational Physics, 2006 219(2): 801–835.Google Scholar
[3] Morrow, R. Space-chargeeffectsin high-density plasmas. Journal of Computational Physics, 1982 46(3): 454–461.Google Scholar
[4] Georghiou, G., Morrow, R., Metaxas, A. A two-dimensional, finite-element, flux-corrected transport algorithm for the solution of gas discharge problems. Journal of Physics D: Applied Physics, 2000 33(19): 2453–2466.CrossRefGoogle Scholar
[5] Min, W., Kim, H., Lee, S., et al. An investigation of FEM-FCT method for streamer corona Simulation. IEEE Transactions on Magnetics, 2000 36(4): 1280–1284.Google Scholar
[6] Boris, J., Book, D. Flux-corrected transport I: SHASTA, a fluid transport algorithm that works. Journal of Computational Physics, 1973 11(1): 38–69.Google Scholar
[7] Zalezak, S. Fully multidimensional flux-corrected transport algorithms for fluids. Journal of Computational Physics, 31(11): 335–362 (1979).Google Scholar
[8] Lohner, R., Morgan, K., Vahdati, M., et al. FEM-FCT: combining unstructured grids with high resolution. Communications in Applied Numerical Methods, 4(6): 717–730 (1988).Google Scholar
[9] Bessieres, D., Paillol, J., Bourdon, A., et al. A new one-dimensional moving mesh method applied to the simulation of streamer discharges. Journal of Physics D: Applied Physics, 40: 6559–6570 (2007).Google Scholar
[10] Pancheshnyi, S., Segur, P., Capeilleŕe, J., et al. Numerical simulation of filamentary discharges with parallel adaptive mesh refinement. Journal of Computational Physics, 227: 6574–6590 (2008).CrossRefGoogle Scholar
[11] Swarztrauber, P. The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equation on a rectangle. SIAM Review, 19(3): 490–501 (1977).CrossRefGoogle Scholar
[12] Bourdon, A., Bessieres, D., Paillol, J., et al. Influence of numerical schemes on positive streamer propagation. Proceedings of 15th Internal Conference on Gas Discharges and their Applications, Toulouse, France, 2004.Google Scholar
[13] Strang, G. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, 5(3): 506–517 (1968).Google Scholar
[14] Shu, C. W. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory schemes for hyperbolic conservation laws. in: Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (Lecture Notes in Mathematics), 1697: 325–432 (1998).CrossRefGoogle Scholar
[15] Zhang, X. and Shu, C.W. Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. Journal of Computational Physics, 231(5): 2245–2258 (2012).Google Scholar
[16] Zhang, X. and Shu, C.W. On maximum-principle-satisfying high order schemes for scalar conservation laws. Journal of Computational Physics, 229(1): 3091–3120 (2010).Google Scholar
[17] Zhang, X. Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws. PhD Thesis, RI: Brown University, 2011.Google Scholar
[18] Zhang, X. and Shu, C.W. Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: survey and new developments. Proceedings of the Royal Society A, 467: 2752–2776 (2011).Google Scholar
[19] Shu, C.W. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statical Computing, 9(6): 1073–1084 (1988).Google Scholar
[20] Dhali, S. and Williams, P. Numerical simulation of streamer propagation in nitrogen at atmospheric pressure. Physical Review A, 31(2): 1219–1222 (1985).Google Scholar
[21] Dhali, S. and Williams, P. Two dimensional studies of streamers in gases. Journal of Applied Physics, 62, 4696 (1987).Google Scholar
[22] Ducasse, O., Papageorghiou, L., Eichwald, O., et al. Critical analysis on two-dimensional point-to-plane streamer simulations using the finite element and finite volume methods. IEEE Transactions on Plasma Science, 35(5): 1287–1300 (2007).Google Scholar
[23] Sweby, P. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 21(5): 995–1011 (1984).Google Scholar