Boltzmann type schemes for gas dynamics and the entropy property
SIAM Journal on Numerical Analysis
Numerical passage from kinetic to fluid equations
SIAM Journal on Numerical Analysis
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
SIAM Journal on Numerical Analysis
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Coupling Boltzmann and Navier-Stokes equations by half fluxes
Journal of Computational Physics
Coupling of the Boltzmann and Euler equations with automatic domain decomposition
Journal of Computational Physics
An implicit Monte Carlo method for rarefied gas dynamics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Time Relaxed Monte Carlo Methods for the Boltzmann Equation
SIAM Journal on Scientific Computing
A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation
Journal of Computational Physics
A smooth transition model between kinetic and hydrodynamic equations
Journal of Computational Physics
Implicit—Explicit Schemes for BGK Kinetic Equations
Journal of Scientific Computing
A moving interface method for dynamic kinetic-fluid coupling
Journal of Computational Physics
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
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In some recent works [G. Dimarco and L. Pareschi, Comm. Math. Sci., 1 (2006), pp. 155-177; Multiscale Model. Simul., 6 (2008), pp. 1169-1197] we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems. Here, in contrast to previous methods, we construct a method form-fitting to any type of finite volume or finite difference scheme for the reduced equilibrium system. Thanks to the coupling of Monte Carlo techniques for the solution of the kinetic equations with macroscopic methods for the limiting fluid equations, we show how it is possible to solve multiscale fluid dynamic phenomena faster than using traditional deterministic/stochastic methods for the full kinetic equations. In addition, due to the hybrid nature of the schemes, the numerical solution is affected by fewer fluctuations than are standard Monte Carlo schemes. Applications to the Boltzmann-BGK equation are presented to show the performance of the new methods in comparison with classical approaches used in the simulation of kinetic equations.