Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Numerical simulations for radiation hydrodynamics. I. diffusion limit
Journal of Computational Physics
Time step size selection for radiation diffusion calculations
Journal of Computational Physics
Journal of Computational Physics
Numerical Modeling in Applied Physics and Astrophysics
Numerical Modeling in Applied Physics and Astrophysics
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
A second order primitive preconditioner for solving all speed multi-phase flows
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics
Journal of Computational Physics
Hi-index | 31.45 |
We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods [2,1,3]) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method [5,20,17]. This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.