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Two viewpoints on the quasi time-consistent filter show that the filtered hyperbolic moment equations is a solver of the Vlasov equation, and it can predict correct physical phenomena described by Vlasov–Poisson equations

Filtered Hyperbolic Moment Method for the Vlasov Equation

Journal of Scientific Computing, no. 2 (2019): 969.0-991.0

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摘要

In this paper, we investigate the effect of the filter for the hyperbolic moment equations (HME) (Cai et al. in Commun Pure Appl Math 67(3):464–518, 2014; Cai et al. in SIAM J Sci Comput 35(6):A2807–A2831, 2013) of the Vlasov–Poisson equations and propose a novel quasi time-consistent filter to suppress the numerical recurrence effect. By...更多

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简介
  • The Vlasov equation is the fundamental kinetic equation modeling of the collisionless plasma.
  • It describes the time evolution of the distribution function f (t, x, v) of a population of charged particles that responds to the self-consistent electromagnetic fields.
  • The distribution function f (t, x, v) is the number density of the particles at the time t and position x ∈ ⊂ RD with the microscopic velocity v ∈ RD [48].
重点内容
  • The Vlasov equation is the fundamental kinetic equation modeling of the collisionless plasma
  • Using the same argument in Sect. 3.2.1, it can be claimed that the filtered hyperbolic moment equations (HME) is a solver of the Vlasov equation and its solution converges to that of the Vlasov equation as M → ∞
  • To study the convergence of the filtered HME and whether the filter changes the Landau damping rate, we provided two viewpoints: artificial collision operator in Sect. 3.2.1 and artificial dissipation in Sect. 3.2.2 to show that the filtered HME is a solver of the Vlasov equation and can predict the correct Landau damping rate and frequency
  • We presented a filtered HME for the Vlasov–Poisson equations to suppress the recurrence effects
  • Due to the careful construction, the filter preserves most of the physical properties of HME, including the conservation of mass, momentum and energy, Galilean invariant and convergence to Vlasov–Poisson equations (VP)
  • Two viewpoints on the quasi time-consistent filter show that the filtered HME is a solver of the Vlasov equation, and it can predict correct physical phenomena described by VP
方法
  • Numerical methods for solving the

    Vlasov equation have been extensively studied, see for instance [5,24,29,49] and references therein.
  • With the exponential growth of computing power, the Eulerian numerical methods attract more and more researchers’ attention, and a lot of methods are developed, for example, the continuous finite element methods [49], finite difference methods [14,22], finite volume methods [23], discontinuous Galerkin methods [29,43], the semi-Lagrangian methods [46] and spectral methods [6,10,44]
  • These methods discretize or approximate the distribution function both in the spatial space and the microscopic velocity space, and they can be used to solve the case that the distribution function has the low-density velocity much more accurately compared to PIC, but may be quite expensive in the high dimension problem
结论
  • The authors presented a filtered HME for the Vlasov–Poisson equations to suppress the recurrence effects.
  • The quasi time-consistent property guarantees that the solution to the filtered HME is not sensitive to the time step.
  • Two viewpoints on the quasi time-consistent filter show that the filtered HME is a solver of the Vlasov equation, and it can predict correct physical phenomena described by VP.
  • Numerical simulations demonstrate the power of the filter in suppressing recurrences and producing more accurate solutions.
基金
  • Di is supported in part by the Natural Science Foundation of China (Grant Nos. 11771437 and 91630208)
  • Wang is supported in part by the Natural Science Foundation of China No 11501042
  • Li is supported in part by the National Natural Science Foundation of China (Grant No 9163030002)
引用论文
  • Adjerid, S., Flaherty, J.E.: A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations. SIAM J. Numer. Anal. 23(4), 778–796 (1986)
    Google ScholarLocate open access versionFindings
  • Armstrong, T.P.: Numerical studies of the nonlinear Vlasov equation. Phys. Fluids 10, 1269–1280 (1967)
    Google ScholarLocate open access versionFindings
  • Armstrong, T.P., Harding, R.C., Knorr, G., Montgomery, D.: Solution of Vlasov’s equation by transform methods. J. Sci. Comput. 9, 29–86 (1970)
    Google ScholarLocate open access versionFindings
  • Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511–525 (1954)
    Google ScholarLocate open access versionFindings
  • Birdsall, C.K., Langdon, A.B.: Plasma Physics Via Computer Simulation. McGraw-Hill, New York (2004)
    Google ScholarFindings
  • Bourdiec, S.L., Vuyst, F.D., Jacquet, L.: Numerical solution of the Vlasov–Poisson system using generalized Hermite functions. Commun. Comput. Phys. 175(8), 528–544 (2006)
    Google ScholarLocate open access versionFindings
  • Cai, Z., Fan, Y., Li, R.: Globally hyperbolic regularization of Grad’s moment system. Commun. Pure Appl. Math. 67(3), 464–518 (2014)
    Google ScholarLocate open access versionFindings
  • Cai, Z., Fan, Y., Li, R.: From discrete velocity model to moment method. Math. Numer. Sin. 38(3), 227–244 (2016)
    Google ScholarLocate open access versionFindings
  • Cai, Z., Fan, Y., Li, R., Lu, T., Wang, Y.: Quantum hydrodynamic model by moment closure of Wigner equation. J. Math. Phys. 53(10), 103503 (2012)
    Google ScholarLocate open access versionFindings
  • Cai, Z., Li, R., Wang, Y.: Solving Vlasov equation using NRx x method. SIAM J. Sci. Comput. 35(6), A2807–A2831 (2013)
    Google ScholarLocate open access versionFindings
  • Cai, Z., Wang, Y.: Suppression of recurrence in the Hermite-spectral method for transport equations. SIAM J. Numer. Anal. 56(5), 3144–3168 (2018)
    Google ScholarLocate open access versionFindings
  • Camporeale, E., Delzanno, G.L., Bergen, B.K., Moulton, J.D.: On the velocity space discretization for the Vlasov–Poisson system: comparison between implicit Hermite spectral and particle-in-cell methods. Commun. Comput. Phys. 198, 47–58 (2016)
    Google ScholarLocate open access versionFindings
  • Canuto, C., Hussaini, M.Y., Quarteroni, A.M., Thomas Jr., A., et al.: Spectral Methods in Fluid Dynamics. Springer, Berlin (2012)
    Google ScholarFindings
  • Carrillo, J., Gamba, M., Majorana, A., Shu, C.: A WENO-solver for the transients of Boltzmann–Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods. J. Comput. Phys. 184, 498–525 (2003)
    Google ScholarLocate open access versionFindings
  • Cheng, C.Z., Knorr, G.: The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330–351 (1976)
    Google ScholarLocate open access versionFindings
  • Cheng, Y., Gamba, M., Morrison, J.: Study of conservation and recurrence of Runge–Kutta discontinuous Galerkin schemes for Vlasov–Poisson systems. J. Sci. Comput. 56, 319–349 (2013)
    Google ScholarLocate open access versionFindings
  • Crouseilles, N., Filbet, F.: Numerical approximation of collisional plasmas by high order methods. J. Comput. Phys. 201(2), 546–572 (2004)
    Google ScholarLocate open access versionFindings
  • Di, Y., Fan, Y., Li, R.: 13-moment system with global hyperbolicity for quantum gas. J. Stat. Phy. 167(5), 1280–1302 (2017)
    Google ScholarLocate open access versionFindings
  • Di, Y., Kou, Z., Li, R.: High order moment closure for Vlasov–Maxwell equations. Front. Math. China 10(5), 1087–1100 (2015)
    Google ScholarLocate open access versionFindings
  • Eliasson, B.: Numerical simulations of the Fourier-transformed Vlasov–Maxwell system in higher dimensions theory and applications. Transp. Theory Stat. Phys. 39(5–7), 387–465 (2010)
    Google ScholarLocate open access versionFindings
  • Ellasson, B.: Outflow boundary conditions for Fourier transformed one-dimensional Vlasov–Poisson system. J. Sci. Comput. 16, 1–28 (2001)
    Google ScholarLocate open access versionFindings
  • Fatemi, E., Odeh, F.: Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices. J. Comput. Phys. 108(2), 209–217 (1993)
    Google ScholarLocate open access versionFindings
  • Filbet, F.: Convergence of a finite volume scheme for the Vlasov–Poisson system. SIAM J. Numer. Anal. 39(4), 1146–1169 (2001)
    Google ScholarLocate open access versionFindings
  • Filbet, F., Sonnendrücker, E.: Comparison of Eulerian Vlasov solvers. Comput. Phys. Commun. 150(3), 247–266 (2003)
    Google ScholarLocate open access versionFindings
  • Filbet, F., Sonnendrücker, E., Bertrand, P.: Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172, 166–187 (2001)
    Google ScholarLocate open access versionFindings
  • Gottlieb, D., Hesthaven, J.S.: Spectral methods for hyperbolic problems. J. Comput. Appl. Math. 128, 83–131 (2001)
    Google ScholarLocate open access versionFindings
  • Grad, H.: On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2(4), 331–407 (1949)
    Google ScholarLocate open access versionFindings
  • Grant, F.C., Feix, M.R.: Fourier-Hermite solutions of the Vlasov equations in the linearized limit. Phy. Fluids 10(4), 696–702 (1967)
    Google ScholarLocate open access versionFindings
  • Heath, R.E., Gamba, I.M., Morrison, P.J., Michler, C.: A discontinuous Galerkin method for the Vlasov–Poisson system. J. Comput. Phys. 231(4), 1140–1174 (2012)
    Google ScholarLocate open access versionFindings
  • Hesthaven, J.S., Kirby, R.: Filtering in Legendre spectral methods. Math. Comput. 77(263), 1425–1452 (2008) 31. 25(1), 1–32 (1996)
    Google ScholarLocate open access versionFindings
  • 32. Hou, T., Li, R.: Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226(1), 379–397 (2007)
    Google ScholarLocate open access versionFindings
  • 33. Joyce, G., Knorr, G., Meier, H.K.: Numerical integration methods of the Vlasov equation. J. Comput. Phys. 8(1), 53–63 (1971)
    Google ScholarLocate open access versionFindings
  • 34. Kanevsky, A., Carpenter, K., Hesthaven, J.S.: Idempotent filtering in spectral and spectral element methods. J. Comput. Phys. 220(1), 41–58 (2006)
    Google ScholarLocate open access versionFindings
  • 35. Klimas, A.J.: A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions. J. Comput. Phys. 68(1), 202–226 (1987)
    Google ScholarLocate open access versionFindings
  • 36. Klimas, A.J., Farrell, W.M.: A splitting algorithm for Vlasov simulation with filamentation filtration. J. Comput. Phys. 110(1), 150–163 (1994)
    Google ScholarLocate open access versionFindings
  • 37. Kreiss, H.O., Oliger, J.: Stability of the Fourier method. SIAM J. Numer. Anal. 16, 421–433 (1979)
    Google ScholarLocate open access versionFindings
  • 38. Landau, L.: On the vibrations of the electronic plasma. Eur. J. Org. Chem. 2006(2), 498–506 (1946) 39. McClarren, R.G., Hauck, C.D.: Robust and accurate filtered spherical harmonics expansions for radiative transfer. J. Comput. Phys. 229(16), 5597–5614 (2010)
    Google ScholarLocate open access versionFindings
  • 40. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, Second Edition, Volume 37 of Springer tracts in natural philosophy. Springer, New York (1998)
    Google ScholarFindings
  • 41. Ng, C.S., Bhattacharjee, A., Skiff, F.: Complete spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 92(6), 065002 (2004)
    Google ScholarLocate open access versionFindings
  • 42. Parker, J.T., Dellar, P.J.: Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit. J. Plasma Phys. 81(02), 305810203 (2015)
    Google ScholarLocate open access versionFindings
  • 43. Qiu, J., Shu, C.: Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov–Poisson system. J. Comput. Phys. 230(23), 8386–8409 (2011)
    Google ScholarLocate open access versionFindings
  • 44. Schumer, J.W., Holloway, J.P.: Vlasov simulation using velocity-scaled Hermite representations. J. Comput. Phys. 144(2), 626–661 (1998)
    Google ScholarLocate open access versionFindings
  • 45. Shoucri, M., Knorr, G.: Numerical integration of the Vlasov equation. J. Comput. Phys. 14(1), 84–92 (1974) Journal of Scientific Computing 46.
    Google ScholarLocate open access versionFindings
  • Sonnendrücker, E., Roche, J., Betrand, P., Ghizzo, A.: The semi-Lagrangian method for the numerical resolution of Vlasov equations. J. Comput. Phys 149(2), 201–220 (1998)
    Google ScholarLocate open access versionFindings
  • 47. Torrilhon, M.: Two dimensional bulk microflow simulations based on regularized Grad’s 13-moment equations. SIAM J. Multiscale Model. Simul. 5(3), 695–728 (2006)
    Google ScholarLocate open access versionFindings
  • 48. Vlasov, A.A.: On vibration properties of electron gas. J. Exp. Theor. Phys. 8(3), 291 (1938)
    Google ScholarLocate open access versionFindings
  • 49. Zaki, S.I., Gardner, R.T., Boyd, T.J.: A finite element code for the simulation of one-dimensional Vlasov plasmas. I. Theory. J. Comput. Phys. 79, 184–199 (1988)
    Google ScholarLocate open access versionFindings
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