TY - JOUR

T1 - A second order self-consistent IMEX method for radiation hydrodynamics

AU - Kadioglu, Samet Y.

AU - Knoll, Dana A.

AU - Lowrie, Robert B.

AU - Rauenzahn, Rick M.

PY - 2010/11

Y1 - 2010/11

N2 - We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods [2,1,3]) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method [5,20,17]. This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.

AB - We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods [2,1,3]) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method [5,20,17]. This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.

KW - Radiation hydrodynamics

KW - Self-consistent IMEX method

UR - http://www.scopus.com/inward/record.url?scp=77956400173&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2010.07.019

DO - 10.1016/j.jcp.2010.07.019

M3 - Article

AN - SCOPUS:77956400173

SN - 0021-9991

VL - 229

SP - 8313

EP - 8332

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 22

ER -