Fully implicit 1D radiation hydrodynamics: Validation and verification

doi:10.1016/j.jcp.2010.06.031

2010-09-01

PRE

Karabi Ghosh *

Suresh Menon

DOI：10.1016/j.jcp.2010.06.031

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摘要

En 中文

A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tri-diagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry. Results obtained when radiation interaction is also accounted agree with those of point explosion with heat conduction for lower input energies. Having, thus, benchmarked the code, self convergence of the method w.r.t. time step is studied in detail for both the planar and spherical problems. Spatial as well as temporal convergence rates are similar or equal to 1 as expected from the difference forms of mass, momentum and energy conservation equations. This shows that the asymptotic convergence rate of the code is realized properly. (C) 2010 Elsevier Inc. All rights reserved.

Keyword:

Implicit radiation hydrodynamics

Lagrangian meshes

Finite difference scheme

Point explosion problem

Self similar solutions

Asymptotic convergence analysis