High‐order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

• Published in: International journal for numerical methods in fluids 2017-04, Vol.83 (10), p.779-797
• Main Authors: Holec, M., Limpouch, J., Liska, R., Weber, S.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Fluid flow; Fluids; high‐order finite element method; Hydrodynamics; Knudsen number; Mathematical models; multigroup diffusion; nonlocal transport; Photons; Plasmas; radiation coupling; radiation hydrodynamics; Transport
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4288

Summary The nonlocal theory of the radiative energy transport in laser‐heated plasmas of arbitrary ratio of the characteristic inhomogeneity scale length to the photon mean free paths is applied to define the closure relations of a hydrodynamic system. The corresponding transport phenomena cannot be described accurately using the Chapman–Enskog approach, that is, with the usual fluid approach dealing only with local values and derivatives. Thus, we directly solve the photon transport equation allowing one to take into account the effect of long‐range photon transport. The proposed approach is based on the Bhatnagar–Gross–Krook collision operator using the photon mean free path as a unique parameter. Such an approach delivers a calculation efficiency and an inherent coupling of radiation to the fluid plasma parameters in an implicit way and directly incorporates nonequilibrium physics present under the condition of intense laser energy deposition due to inverse bremsstrahlung. In combination with a higher order discontinuous Galerkin scheme of the transport equation, the solution obeys both limiting cases, that is, the local diffusion asymptotic usually present in radiation hydrodynamics models and the collisionless transport asymptotic of free‐streaming photons. In other words, we can analyze the radiation transport closure for radiation hydrodynamics and how it behaves when deviating from the conditions of validity of Chapman–Enskog method, which is demonstrated in the case of exact steady transport and approximate multigroup diffusion numerical tests. As an application, we present simulation results of intense laser‐target interaction, where the radiative energy transport is controlled by the mean free path of photons. Copyright © 2016 John Wiley & Sons, Ltd. Nonlocal radiative transport in laser‐heated plasmas of arbitrary Knudsen number is a challenging task. We directly solve the photon transport equation based on the Bhatnagar‐Gross‐Krook(BGK) collision operator, which gives an inherent coupling of radiation to the fluid plasma parameters. Our high‐order discontinuous Galerkin scheme of the BGK transport equation and thefluid energy equation gives solutions obeying both limiting cases of transport, i.e. diffusion and free‐streaming. As an application, we present simulation results of intense laser‐target interaction.