On the scope of the method of modified equations
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A critical analysis of the modified equation technique of Warming and Hyett
Journal of Computational Physics
Multifrequency-gray method for radiation diffusion with Compton scattering
Journal of Computational Physics
Enslaved finite difference approximations for quasigeostrophic shallow flows
Physica D - Special issue on nonlinear phenomena in ocean dynamics
MPDATA: a finite-difference solver for geophysical flows
Journal of Computational Physics
Time step size selection for radiation diffusion calculations
Journal of Computational Physics
Iterative linear solvers in a 2D radiation-hydrodynamics code: methods and performance
Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Numerical Modeling in Applied Physics and Astrophysics
Numerical Modeling in Applied Physics and Astrophysics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
New physics-based preconditioning of implicit methods for non-equilibrium radiation diffusion
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Studies of the accuracy of time integration methods for reaction-diffusion equations
Journal of Computational Physics
Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
Journal of Computational Physics
Multilevel schemes for the shallow water equations
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
Methods for coupling radiation, ion, and electron energies in grey Implicit Monte Carlo
Journal of Computational Physics
Numerical analysis of time integration errors for nonequilibrium radiation diffusion
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
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
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Hi-index | 31.53 |
The effect of various numerical approximations used to solve linear and nonlinear problems with multiple time scales is studied in the framework of modified equation analysis (MEA). First, MEA is used to study the effect of linearization and splitting in a simple nonlinear ordinary differential equation (ODE), and in a linear partial differential equation (PDE). Several time discretizations of the ODE and PDE are considered, and the resulting truncation terms are compared analytically and numerically. It is demonstrated quantitatively that both linearization and splitting can result in accuracy degradation when a computational time step larger than any of the competing (fast) time scales is employed. Many of the issues uncovered on the simple problems are shown to persist in more realistic applications. Specifically, several differencing schemes using linearization and/or time splitting are applied to problems in nonequilibrium radiation-diffusion, magnetohydrodynamics, and shallow water flow, and their solutions are compared to those using balanced time integration methods.