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
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
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
A second order self-consistent IMEX method for radiation hydrodynamics
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 | 31.46 |
We present a fully second order implicit/explicit time integration technique for solving hydrodynamics coupled with nonlinear heat conduction problems. The idea is to hybridize an implicit and an explicit discretization in such a way to achieve second order time convergent calculations. In this scope, the hydrodynamics equations are discretized explicitly making use of the capability of well-understood explicit schemes. On the other hand, the nonlinear heat conduction is solved implicitly. Such methods are often referred to as IMEX methods [2,1,3]. The Jacobian-Free Newton Krylov (JFNK) method (e.g. [10,9]) is applied to the problem in such a way as to render a nonlinearly iterated IMEX method. We solve three test problems in order to validate the numerical order of the scheme. For each test, we established second order time convergence. We support these numerical results with a modified equation analysis (MEA) [21,20]. The set of equations studied here constitute a base model for radiation hydrodynamics.