Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
A multgrid Newton-Krylov method for multimaterial equilibrium radiation diffusion
Journal of Computational Physics
Time step size selection for radiation diffusion calculations
Journal of Computational Physics
An implicit energy-conservative 2D Fokker-Planck algorithm: II. Jacobian-free Newton—Krylov solver
Journal of Computational Physics
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
Studies of the accuracy of time integration methods for reaction-diffusion equations
Journal of Computational Physics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
A deterministic photon free method to solve radiation transfer equations
Journal of Computational Physics
Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D
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
A 3-D multiband closure for radiation and neutron transfer moment models
Journal of Computational Physics
Semi-implicit time integration for PN thermal radiative transfer
Journal of Computational Physics
Short Note: On 1D diffusion problems with a gradient-dependent diffusion coefficient
Journal of Computational Physics
Second-order time evolution of PN equations for radiation transport
Journal of Computational Physics
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Journal of Scientific Computing
Nonlinear variants of the TR/BDF2 method for thermal radiative diffusion
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
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
Journal of Computational Physics
Hi-index | 31.52 |
Several time integration methods for nonlinear systems are compared. All of the time discretizations are based on the θ-method, but differ in their treatment of the implicit nonlinear terms. One method converges the implicit nonlinear terms to a small tolerance and is often referred to as nonlinearly consistent (NC). Newton's method, or its approximation Newton-Krylov, is used to converge the nonlinearities. The other methods considered are linearized and comparisons are made for a relaxation problem and a radiation diffusion problem. The linearized one-step method that uses the full Jacobian is shown to have similar accuracy as NC methods. The lagged linearization method and an extension that is second-order accurate are also studied. A trunction error analysis complements the numerical results, For the relaxation problem, it is shown that each of the second-order accurate linearized methods may be more accurate than an NC method, depending on the degree of nonlinearity in the problem. For the radiation diffusion problem, in general the NC method is most accurate and allows a larger time step. However, the linearized methods perfom surprisingly well.