Combine Hydrodynamics and Electromagnetics

Question

Is it possible, in general, to combine hydrodynamical motion and expansion of material with, say, a finite difference time domain method to simulate light-matter interaction?

If so, how is this done in practice? I guess you would need some kind of operator splitting scheme. If you know more about it, can you suggest me some papers, textbooks, etc.?

Answer 1

Regarding simulation: There are several commercial solvers that might be helpful.

• A very popular FDTD Maxwell equation solvers for nanophotonics is Lumerical. It features opto-thermal and liquid crystal (which I would say is another keyword you should consider) simulations that should be very relevant.

• Another go-to multiphysics solver would be COMSOL. Searching for electrohydrodynamics and magnetohydrodynamics will results in a lot of results. Several relevant papers for COMSOL-based modeling:

  1. M. G. Sailer, B. J. Kirby, "Computational simulation of electrohydrodynamic systems pertaining to micro and nano scale fluid flow phenomenon," in Proc. COMSOL Conf., Boston, MA, 2008.
  2. A. Mulye, S. Potnis, "Electrohydrodynamic micropump modeling for performance optimization," in Proc. COMSOL Conf., Bangalore, India, 2013.
  3. N. Kleinknecht, "High frequency magnetohydrodynamic calculations in COMSOL," in Proc. COMSOL Conf., Stuttgart, Germany, 2011.
  4. Y. Yan, S. Smolentsev, M. Abdou, "Validation of COMSOL multiphysics for magnetohydrodynamics (MHD) flows in fusion applications," in Proc. COMSOL Conf., Boston, MA, 2017.

Regarding numerical techniques themselves:

• I recently stumbled upon the following paper (that was my main motivation even to write an answer to your question): E. Veerapaneni, "Integral equation methods for vesicle electrohydrodynamics in three dimensions," J. Comp. Phys., vol. 326, pp. 278-289, Dec. 2016. From its abstract: The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.
• And another paper that crossed my eyes several years ago that features numerical study in magnetohydrodynamics: M. Kinet, B. Knaepen, and S. Molokov, "Instabilities and transition in magnetohydrodynamic flows in ducts with electrically conducting walls," Phys. Rev. Lett., vol. 103, 154501, Oct. 2009.