A fully second order implicit/explicit time integration technique for hydrodynamics plus nonlinear heat conduction problems. (English) Zbl 1307.76056

Summary: 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. The Jacobian-Free Newton Krylov (JFNK) method 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). The set of equations studied here constitute a base model for radiation hydrodynamics.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics (general theory)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
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