Iterative Implementation of an Implicit–Explicit Hybrid Scheme for Hydrodynamics

Numerical Simulations for Radiation Hydrodynamics. I. Diffusion Limit

“…We should mention that the extra half time step and the interpolation based on the values at t/2 and t were first introduced in [23] for gas dynamics and are iteratively implemented in [30]. Compared to two typical implicit schemes, the backward Euler and the Crank-Nicolson schemes, the number of unknown variables has been doubled in Eqs.…”

Numerical Simulations for Radiation Hydrodynamics

“…In this paper, an iterative approach is developed for the set of nonlinear algebraic equations arising from the implicitness of the scheme. Compared to the iterative approach developed in [38,39], the number of iterations needed is reduced by more than one order. No matter how many cells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme.…”

“…Wilcoxson and Manousiouthakis [31] developed implicit time marching implementation of the essentially non-oscillatory scheme. Dai and Woodward [38,39] iteratively implemented an implicit-explicit hybrid scheme.…”

Numerical Simulations for Nonlinear Heat Transfer in a System of Multimaterials

“…Resolving shock fronts is one of major difficulties in gas dynamics, which was handled through an approximate Riemann solver. The schemes in [20,25] are good only for hyperbolic systems of conservation laws, and only a single kind of material is considered in [20,25]. Since the Euler equations describe nonlinear wave interactions, a multicolor relaxation, instead of the multigrid method, has been used in [25] for the fast convergence of iterations.…”

“…The time discretization to be presented in this paper is adopted from the implicit-explicit hybrid schemes [20,25] for the Euler equations in gas dynamics. Resolving shock fronts is one of major difficulties in gas dynamics, which was handled through an approximate Riemann solver.…”