Meshfree method for fluctuating hydrodynamics. (English) Zbl 1252.76025
Summary: In the current study a meshfree Lagrangian particle method for the Landau-Lifshitz Navier-Stokes (LLNS) equations is developed. The LLNS equations incorporate thermal fluctuation into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation theorem. The study focuses on capturing the correct variance and correlations computed at equilibrium flows, which are compared with available theoretical values. Moreover, a numerical test for the random walk of standing shock wave has been considered for capturing the shock location.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q30 | Navier-Stokes equations |
Keywords:
Landau-Lifshitz Navier-Stokes equations; fluctuating hydrodynamics; finite pointset method; stochastic fluxes; covariancesReferences:
| [1] | Alexander, F. J.; Garcia, A. L.; Tartakovsky, D. M., Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, Journal of Computational Physics, 182, 1, 47-66 (2002) · Zbl 1090.65510 |
| [2] | Alexander, F. J.; Garcia, A. L.; Tartakovsky, D. M., Algorithm refinement for stochastic partial differential equations: II. Correlated systems, Journal of Computational Physics, 207, 769-787 (2005) · Zbl 1072.65006 |
| [3] | Bell, J.; Foo, J.; Garcia, A. L., Algorithm refinement for the stochastic burgers’ equation, Journal of Computational Physics, 223, 451-468 (2007) · Zbl 1113.65007 |
| [4] | Bell, J. B.; Garcia, A. L.; Williams, S. A., Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations, Physical Review E, 76, 016708 (2007) |
| [5] | Bixon, M.; Zwanzig, R., Boltzmann-Langevin equation and hydrodynamic fluctuations, Physical Review, 187, 267-272 (1969) |
| [6] | Eggers, J., Dynamic of liquid nanojets, Physical Review Letters, 89, 084502 (2002) |
| [7] | Fabritiis, G. D.; Coveney, P. V.; Flekky, E. G., Multiscale dissipative particle dynamics, Philosophical Transactions of the Royal Society of London, Series A, 360, 317-331 (2002) · Zbl 0996.82053 |
| [8] | Fabritiis, G. D.; Delgado-Buscalioni, R.; Coveney, P. V., Multiscale modeling of liquid with molecular specificity, Physical Review Letters, 97, 13, 134501 (2006) |
| [9] | Fox, R. F.; Uhlenbeck, G. E., Contributions to non-equilibrium thermodynamics. i. Theory of hydrodynamical fluctuations, Physics of Fluids, 13, 8, 1893-1902 (1970) · Zbl 0209.57503 |
| [10] | Garcia, A. L.; Mansour, M. M.; Lie, G. C.; Clementi, E., Numerical integration of the fluctuating hydrodynamics equations, Journal of Statistical Physics, 47, 209-228 (1987) · Zbl 0681.76009 |
| [11] | Ho, C. M.; Tai, Y. C., Micro-electro-mechanical system (mems) and fluid flow, Annual Review of Fluid Mechanics, 30, 579-612 (1998) |
| [12] | Karniadakis, G.; Beskok, A.; Aluru, N., Microflows and Nanoflows: Fundamentals and Simulation (2005), Springer: Springer New York · Zbl 1115.76003 |
| [13] | Kelly, G. E.; Lewis, M. B., Hydrodynamics fluctuations, Physics of Fluids, 14, 9, 925-1931 (1971), 1 · Zbl 0231.76032 |
| [14] | Ladd, A. J.C., Short-time motion of colloidal particles: numerical simulation via a fluctuating lattice-Boltzmann equation, Physical Review Letters, 70, 9, 1339-1342 (1993) |
| [15] | Landau, L.; Lifshitz, E., Fluid mechanics, Course of Theoretical Physics, vol. 6 (1959), Pergamon |
| [16] | Landau, L. D.; Lifshitz, E. M., Statistical Physics, Course of Theoretical Physics, vol. 5 (1980), Pergamon: Pergamon New York |
| [17] | Moseler, M.; Landman, U., Formation, stability, and breakup of nanojets, Science, 289, 5482, 1165-1169 (2000) |
| [18] | nol, P. E., Stochastic differential equations for non-linear hydrodynamics, Physica A, 248, 77-96 (1998) |
| [19] | Serrano, M.; nol, P. E., Thermodynamically consistent mesoscopic fluid particle model, Physical Review E, 64, 4, 046115 (2001) |
| [20] | Sharma, N.; Patankar, N. A., Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamics equations, Journal of Computational Physics, 201, 2, 466-486 (2004) · Zbl 1061.76086 |
| [21] | Tiwari, S., A lsq-sph approach for solving compressible viscous flow, International Series of Numerical Mathematics, 141 (2000) |
| [22] | Tiwari, S.; Antonov, S.; Hietel, D.; Kuhnert, J.; Wegener, R., A meshfree method for simulations of interactions between fluids and flexible structures, Lecture Notes in Computational Science and Engineering, 57 (2006), (Meshfree Methods for Partial Differential Equations III) |
| [23] | Williams, S.; Bell, J.; Garcia, A. L., Algorithm refinement for fluctuating hydrodynamics, SIAM Multiscale Modeling and Simulation, 6, 1256-1280 (2008) · Zbl 1247.76065 |
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