Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Accurate semi-implicit treatment of the hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Derivation of implicit difference schemes by the method of differential approximation
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Enhanced Nonlinear Iterative Techniques Applied to a Nonequilibrium Plasma Flow
SIAM Journal on Scientific Computing
A multilevel iterative field solver for implicit, kinetic, plasma simulation
Journal of Computational Physics
A Multigrid Preconditioned Newton--Krylov Method
SIAM Journal on Scientific Computing
An implicit energy-conservative 2D Fokker-Planck algorithm: II. Jacobian-free Newton—Krylov solver
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
On Preconditioning Newton--Krylov Methods in Solidifying Flow Applications
SIAM Journal on Scientific Computing
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
A fully implicit, nonlinear adaptive grid strategy
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
Hall magnetohydrodynamics on block-adaptive grids
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Journal of Computational Physics
Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Hi-index | 31.51 |
A nonlinear, fully implicit solver for a 2D high-β (incompressible) Hall magnetohydrodynamics (HMHD) model is proposed. The task in non-trivial because HMHD supports the whistler wave. This wave is dispersive (ω ˜ k2) and therefore results in diffusion-like numerical stability limits for explicit time integration methods. For HMHD, implicit approaches using time steps above the explicit numerical stability limits result in diagonally submissive Jacobian systems. Such systems are difficult to invert with iterative techniques. In this study, Jacobian-free Newton-Krylov iterative methods are employed for a fully implicit, nonlinear integration, and a semi-implicit (SI) preconditioner strategy, developed on the basis of a Schur complement analysis, is proposed. The SI preconditioner transforms the coupled hyperbolic whistler system into a fourth-order, parabolic, diagonally dominant PDE, amenable to iterative techniques. Efficiency and accuracy results are presented demonstrating that an efficient fully implicit implementation (i.e., faster than explicit methods) is indeed possible without sacrificing numerical accuracy.