Nonoscillatory interpolation methods applied to Vlasov-based models

SIAM Journal on Scientific Computing

Volumn 29, Issue 3, 2007, Pages 1179-1206

  Carrillo, J A ^a   Vecil, F ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Flux balance method; Kinetic equations; Semi Lagrangian method; Strang's splittings; Vlasov equations; WENO

Indexed keywords

FINITE DIFFERENCE METHOD; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; PROBLEM SOLVING; SEMICONDUCTOR MATERIALS;

KINETIC EQUATIONS; SEMI-LAGRANGIAN METHOD; VLASOV EQUATIONS; WENO;

INTERPOLATION;

EID: 44649190380     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050644549     Document Type: Article

References (30)

1. R. ABGRALL AND C. BASDEVANT, A semi-Lagrangian numerical scheme for two-dimensional turbulence, C. R. Acad. Sci. Paris Sér. I Math., 305 (1987), pp. 315-318.
2. J. R. BATES, Semi-Lagrangian advective schemes and their use in meteorological modeling, in Large-Scale Computations in Fluid Mechanics, Part 1 (La Jolla, CA, 1983), Lectures in Appl. Math. 22-1, AMS, Providence, RI, 1985, pp. 1-29.
3. N. BESSE AND E. SONNENDRÜCKER, Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space, J. Comput. Phys., 191 (2003), pp. 341-376.
4. J. A. CARRILLO, M. J. CÁCERES, AND T. GOUDON, Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles, Comm. Partial Differential Equations, 28 (2003), pp. 969-989.
5. J. A. CARRILLO, I. M. GAMBA, A. MAJORANA, AND C. W. SHU, A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods, J. Comput. Phys., 184 (2003), pp. 498-525.
6. J. A. CARRILLO, I. M. GAMBA, A. MAJORANA, AND C. W. SHU, 2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions, and comparison to Monte Carlo methods, J. Comput. Phys., 214 (2006), pp. 55-80.
7. J. A. CARRILLO, I. GAMBA, AND C W. SHU, Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors, Phys. D, 146 (2000), pp. 289-306.
8. C. CERCIGNANI, I. GAMBA, J. JEROME, AND C. W. SHU, Device benchmark comparisons via kinetic, hydrodynamic, and high-field models, Comput. Methods Appl. Mech. Engrg., 181 (2000), pp. 381-392.
9. C. Z. CHENG AND G. KNORR, The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22 (1976), pp. 330-348.
10. N. CROUSEILLES AND F. FILBET, Numerical approximation of collisional plasmas by high order methods, J. Comput. Phys., 201 (2004), pp. 546-572.
11. L. DESVILLETTES AND C. VILLANI, On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation, Comm. Pure Appl. Math., 54 (2001), pp. 1-42.
12. 2 N, SIAM J. Sci. Comput., 28 (2006), pp. 1029-1053.
13. F. FILBET AND E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Comput. Phys. Comm., 150 (2003), pp. 247-266.
14. F. FILBET, E. SONNENDRÜCKER, AND P. BERTRAND, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys., 172 (2001), pp. 166-187.
15. M. GUTNIC, M. HAEFELE, I. PAUN, AND E. Sonnendrücker, Vlasov simulations on an adaptive phase-space grid, Comput. Phys. Comm., 164 (2004), pp. 214-219.
16. F. HÉRAU, Hypercoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation, Asymptot. Anal., 46 (2006), pp. 349-359.
17. F. HÉRAU AND F. NIER, Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with high degree potential, Arch. Ration. Mech. Anal., 171 (2004), pp. 151-218.
18. F. HUOT, A. GHIZZO, P. BERTRAND, E. Sonnendrücker, and O. COULAUD, Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system, J. Comput. Phys., 185 (2003), pp. 512-531.
19. G. S. JIANG AND C. W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
20. S. JIN, L. PARESCHI, AND G. TOSCANI, Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Numer. Anal., 38 (2000), pp. 913-936.
21. S. LABRUNIE, J. A. CARRILLO, AND P. BERTRAND, Numerical study on hydrodynamic and quasi-neutral approximations for collisionless two-species plasmas, J. Comput. Phys., 200 (2004), pp. 267-298.
22. L. PARESCHI AND G. RUSSO, Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations, in Recent Trends in Numerical Analysis, L. Brugnano and D. TRIGIANTE, eds., Adv. Theory Comput. Math. 3, Nova Science Publishers, Commack, NY, 2000, pp. 269-288.
23. L. PARESCHI AND G. RUSSO, Implicit-explicit Runge-Kutta methods and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), pp. 129-155.
24. K. SEBASTIAN AND C. W. SHU, Multidomain WENO finite difference method with interpolation at subdomain interfaces, J. Sci. Comput., 19 (2003), pp. 405-438.
25. C.-W. SHU, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. 1697, Springer-Verlag, Berlin, 1998, pp. 325-432.
26. C. W. SHU AND S. OSHER, Efficient implementation of essentially non oscillatory shock capturing schemes J. Comput. Phys., 77 (1988), pp. 439-471.
27. E. SONNENDRÜCKER, J. ROCHE, P. BERTRAND, AND A. GHIZZO, The semi-Lagrangian method for the numerical resolution of the Vlasov equation, J. Comput. Phys., 149 (1999), pp. 201-220.
28. J. STOER AND R. BULIRSCH, Introduction to Numerical Analysis, Springer-Verlag, New York, 1993.
29. G. STRANG, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.
30. T. ZHOU, Y. GUO, AND C. W. SHU, Numerical study on Landau damping, Phys. D, 157 (2001), pp. 322-333.