A fully second order implicit/explicit time integration technique for hydrodynamics plus nonlinear heat conduction problems


Kadioglu S. Y. , KNOLL D. A.

JOURNAL OF COMPUTATIONAL PHYSICS, cilt.229, ss.3237-3249, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 229 Konu: 9
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.jcp.2009.12.039
  • Dergi Adı: JOURNAL OF COMPUTATIONAL PHYSICS
  • Sayfa Sayıları: ss.3237-3249

Özet

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. [10,91) 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. Published by Elsevier Inc.