A Fully Second Order Implicit/Explicit Time Integration Technique for Hydrodynamics Plus Nonlinear Heat Conduction Problems

Abstract

We present a second order non-linearly consistent implicit/explicit time integration tech¬nique for solving hydrodynamics coupled with nonlinear heat conduction problems. The idea is to hybridize an implicit and an explicit discretization in a nonlinearly consistent way in order to achieve second order time convergent calculations. In this scope, the hydrody¬namics 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 nu-merical order of the scheme. For each test, we established second order time convergence. We support these numerical results with a Modi?ed Equation Analysis (MEA) [23,22]. The set of equations studied here constitute a base model for radiation hydrodynamics.