Coupling Boltzmann and Navier-Stokes equations by friction
Journal of Computational Physics
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
Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations
Journal of Computational Physics
Coupling of the Boltzmann and Euler equations with automatic domain decomposition
Journal of Computational Physics
Numerical solution of plasma fluid equations using locally refined grids
Journal of Computational Physics
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Journal of Computational Physics
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
On the construction of kinetic schemes
Journal of Computational Physics
Coupling of the Wang Chang--Uhlenbeck equations with the multispecies Euler system
Journal of Computational Physics
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Journal of Computational Physics
A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation
Journal of Computational Physics
An adaptive grid refinement strategy for the simulation of negative streamers
Journal of Computational Physics
Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
Journal of Computational Physics
A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
Fast numerical method for the Boltzmann equation on non-uniform grids
Journal of Computational Physics
Numerical simulation of filamentary discharges with parallel adaptive mesh refinement
Journal of Computational Physics
On Spatial Orders and Location Codes
IEEE Transactions on Computers
A particle-particle hybrid method for kinetic and continuum equations
Journal of Computational Physics
Journal of Computational Physics
A multiscale kinetic-fluid solver with dynamic localization of kinetic effects
Journal of Computational Physics
A unified gas-kinetic scheme for continuum and rarefied flows
Journal of Computational Physics
A new adaptive mesh refinement data structure with an application to detonation
Journal of Computational Physics
Monte Carlo solution of the Boltzmann equation via a discrete velocity model
Journal of Computational Physics
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Locally refined discrete velocity grids for stationary rarefied flow simulations
Journal of Computational Physics
Local discrete velocity grids for deterministic rarefied flow simulations
Journal of Computational Physics
Hi-index | 31.46 |
This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang-Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.