Numerical Tests and Properties of Waves in Radiating Fluids Page: 3 of 43
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Numerical Tests and Properties of Waves in
Bryan M. Johnson a, b & Richard I. Klein a,c
aLawrence Livermore National Laboratory, AX Division, 7000 East Avenue,
Livermore, CA 94550
CDepartment of Astronomy, University of California, Berkeley 601 Campbell Hall,
Berkeley, CA 94720
We discuss the properties of an analytical solution for waves in radiating fluids,
with a view towards its implementation as a quantitative test of radiation hydrody-
namics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is
periodically driven at the boundary of a one-dimensional domain, and the solution
describes the propagation of the waves thus excited. Two modes are excited for a
given driving frequency, generally referred to as a radiative acoustic wave and a
radiative diffusion wave. While the analytical solution is well known, several fea-
tures are highlighted here that require care during its numerical implementation.
We compare the solution in a wide range of parameter space to a numerical in-
tegration with a Lagrangian radiation hydrodynamics code. Our most significant
observation is that flux-limited diffusion does not preserve causality for waves on a
Key words: radiation hydrodynamics, waves
PA CS: 42.25.Bs, 42.68.Ay, 52.35.Dm, 52.35.Lv
Analytical solutions for radiation hydrodynamics are difficult to obtain due to
the complexity of the equations and have become an increasingly powerful tool
for testing complex multi-physics codes. One of the most useful simplifying
assumptions for any set of nonlinear differential equations is to set up an equi-
librium state and analyze small departures from that equilibrium. Since this
approach retains most of the terms in the equations, it not only provides valu-
able physical insight but also serves as a comprehensive and sensitive test of
Preprint submitted to Elsevier
10 September 2009
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Johnson, B M & Klein, R I. Numerical Tests and Properties of Waves in Radiating Fluids, article, September 3, 2009; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc926935/m1/3/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.