At molecular scales, fluids are inherently noisy with thermally induced fluctuations playing a key role in the dynamics. When mechanical instabilities, chemical reactions and other phenomena at the microscopic scale are sensitive to these fluctuations, fluctuations can affect behavior at larger scales. The goal of this project is to develop algorithms and stochastic hybrid models to simulate these types of multiscale problems arising in fluids. Accurate modeling of these types of multiscale phenomena require the correct decomposition of the component processes for these fluctuations. The correct treatment of fluctuations is especially important for nonlinear systems, such as those undergoing phase transitions, nucleation, barrier-crossing, Brownian motors, noise-driven instabilities, combustive ignition, etc. In these and related applications, nonlinearities can exponentially amplify the influence of fluctuations.
Over the last few years, we have worked in several different areas starting with the development of hybrid algorithms combining DSMC particle schemes with the Landau-Lifshitz fluctuating Navier-Stokes equations to model fluctuations at the continuum level. This was also extended to treat multicomponent systems. The methodology has also been used to model enhancement of diffusive transport under nonequilibrium constraints and in modeling nonreactive multispecies mixtures. We have worked on developing staggered and higher order finite volume schemes for these systems as well. Recently we extended this methodology to developing low mach multicomponent schemes for diffusively mixing fluids and modeling multiphase flows in single component fluids near the critical point.
Our current focus is on extending the existing framework to developing techniques to model recent experiments of mixed-mode instabilities observed in ternary mixtures and model fluctuations in single phase and multiphase electrolyte solutions.
Low Mach Number Fluctuating Hydrodynamics.
In order to study the effects of thermal fluctuations in fluids at the microscale, we have developed a new low Mach number fluctuating hydrodynamics code for multicomponent mixtures. The image on the left shows the development of a mixed-mode instability as a layer of salty water is placed on top of a horizontal layer of less-dense sweet water. The image on the right shows a different configuration where the salty water has been further diluted in water so that denser sweet water lies underneath. Here we see the development of a diffusive layer convection instability. The color plots show the vertically averaged density (horizontal plane) and planar slices of density (vertical planes). The observed giant fluctuations are caused by long-range correlations between fluctuations.
Super-critical Argon undergoing adiabatic cooling (left figure) in a square cavity via the Piston effect, and spinodal decomposition (right figure) when subjected to a critical quench.
A. K. Bhattacharjee, K. Balakrishnan, A. L. Garcia, J. B. Bell, and A. Donev, "Fluctuating hydrodynamics of multispecies reactive mixtures," submitted for publication. [arxiv].
A. Donev, A. Nonaka, A. K. Bhattacharjee, A. L. Garcia, and J. B. Bell, "Low Mach Number Fluctuating Hydrodynamics of Multispecies Liquid Mixtures," Phys. Fluids, 27, 3, 2015. [arxiv].
A. Nonaka, Y. Sun, J. B. Bell, and A. Donev, "Low Mach Number Fluctuating Hydrodynamics of Binary Liquid Mixtures," submitted for publication [pdf].Anuj Chaudhri, John Bell, Alejandro Garcia and Aleksandar Donev "Modeling Multi-Phase Flow using Fluctuating Hydrodynamics", Phys. Rev. E, vol. 90, no. 3, 033014, 2014. [arxiv].
M. Cai, A. Nonaka, B. E. Griffith, J. B. Bell, and A. Donev, "Efficient Variable-Coefficient Finite-Volume Stokes Solvers," accepted for publication in Commun. Comput. Phys., 2014. [pdf]
A. Donev, A. Nonaka, Y. Sun, T. Fai, A. Garcia and J. Bell, "Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids" Comm. App. Math. and Comp. Sci., vol. 9, no. 1, 2014. [pdf]
K. Balakrishnan, A. Garcia, A. Donev, and J. Bell, "Fluctuating hydrodynamics of multispecies nonreactive mixtures" Physical Review E, vol. 89, No. 1, January 2014. [pdf]
F. Balboa Usabiaga, J. Bell, R. Delgado-Buscalioni, A. Donev, T. Fai, B. Griffith, C. Peskin, "Staggered Schemes for Fluctuating Hydodynamics", Multiscale Modeling and Simulation, 10, 4, 1360-1408, 2012. [pdf]
K. Balakrishnan, J.B. Bell, A. Donev, and A. Garcia, "Fluctuating Hydrodynamics and Direct Simulation Monte Carlo", 28th International Symposium on Rarefied Gas Dynamics , AIP Conf. Proc. 1501 , 695-704, 2012. [pdf]
A. Garcia, A. Donev, J.B. Bell, and B. Alder, "Hydrodynamic fluctuations in a particle-continuum hybrid for complex fluids", 27th International Symposium on Rarefied Gas Dynamics , AIP Conf. Proc. 1333 , 551-556, 2011. [pdf]
A. Donev, A. de la Fuente, J. B. Bell, and A. L. Garcia, "Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations", JSTAT, Vol. 2011, P06014, (2011). [pdf]
A. Donev, A. de la Fuente, J. B. Bell, and A. L. Garcia, "Diffusive Transport by Thermal Velocity Fluctuations", Phys. Rev. Lett., Vol. 106, No. 20, page 204501, 2011. [pdf]
A. Donev, J. B. Bell, A. L. Garcia, and B. J. Alder, "A hybrid particle-continuum method for
hydrodynamics of complex fluids," SIAM Multiscale Modeling and Simulation 8 871-911, 2010. [pdf]
A. Donev, E. Vanden-Eijnden, A. Garcia, and J. Bell, "On the Accuracy of Explicit Finite-Volume Schemes for Fluctuating Hydrodynamics," Communications in Applied Mathematics and Computational Science 5 149-197, 2010. [pdf]
J. B. Bell, A. L. Garcia, S. A. Williams, "Computational fluctuating fluid dynamics", ESAIM: Mathematical Modelling and Numerical Analysis, 44 1085-1105, 2010. [pdf]
J. B. Bell, A. L. Garcia, S. A. Williams, S. A. Williams, J. B. Bell, and A. L. Garcia, "Algorithm refinement for fluctuating hydrodynamics", Multiscale Model. Simul. 6, 1256-1280, 2008. [pdf]
John B. Bell, Alejandro L. Garcia and Sarah A. Williams, "Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations", Phys. Rev. E 76, 016708, 2007. [pdf]
J. B. Bell, J. Foo, and A. L. Garcia, "Algorithm Refinement for the Stochastic Burgers' Equation", J. Comp. Phys., 223, pp. 603-708, 2006. [pdf]
A. L. Garcia, J. B. Bell, W. Y. Crutchfield, B. J. Alder, "Adaptive Mesh and Algorithm Refinement,"J. Comp. Phys., 154, pp. 134-155, 1999. [ps.gz]