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Abstract

Recently, thermal fluctuations have been introduced into the Lattice Boltzmann method for non-ideal fluids, allowing one to numerically solve the fluctuating Navier-Stokes equations for an isothermal liquid-vapor system. Here, it is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A particular focus will be on finite-size effects and issues related to the global conservation of the order-parameter. Additionally, the critical behavior of the transport coefficients (speed of sound, shear and bulk viscosity) of the model, which describes an isothermal compressible fluid, is discussed.