Numerical passage from kinetic to fluid equations
SIAM Journal on Numerical Analysis
Coupling Boltzmann and Navier-Stokes equations by half fluxes
Journal of Computational Physics
An adaptive domain decomposition procedure for Boltzmann and Euler equations
Journal of Computational and Applied Mathematics
Coupling of the Boltzmann and Euler equations with automatic domain decomposition
Journal of Computational Physics
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High order numerical methods for the space non-homogeneous Boltzmann equation
Journal of Computational Physics
A hybrid particle-continuum method applied to shock waves
Journal of Computational Physics
Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
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
Journal of Computational Physics
A hybrid particle approach for continuum and rarefied flow simulation
Journal of Computational Physics
A multiscale kinetic-fluid solver with dynamic localization of kinetic effects
Journal of Computational Physics
Journal of Computational Physics
An Asymptotic Preserving Scheme for the ES-BGK Model of the Boltzmann Equation
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Microscopically implicit-macroscopically explicit schemes for the BGK equation
Journal of Computational Physics
Microscopically implicit-macroscopically explicit schemes for the BGK equation
Journal of Computational Physics
Hi-index | 31.45 |
In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used to represent the transition between fully kinetic to equilibrium flows. In this fashion, the Boltzmann solver is used only when the collision integral is non-stiff, and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities. Thus, in principle, the same mesh size and time steps can be used in the whole computation. Moreover, the time step is limited only by convective terms. Since the Boltzmann solver is applied only in wholly kinetic regimes, we use the reduced noise DSMC scheme we have proposed in Part I of the present work. This ensures a smooth exchange of information across the different domains, with a natural way to construct interface numerical fluxes. Several tests comparing our hybrid scheme with full Boltzmann DSMC computations show the good agreement between the two solutions, on a wide range of Knudsen numbers.