Robert B. Lowrie

Issues with high-resolution Godunov methods for radiation hydrodynamics☆

Abstract Two issues in the development of high-resolution Godunov methods for radiation hydrodynamics are discussed. First, an analysis of the Riemann problem is given. Second, it is shown that a large class of commonly used high-resolution methods are unable to obtain the equilibrium diffusion limit. The analysis points to several possible fixes.

Analysis of Ray-Effect Mitigation Techniques

Abstract We analyze three ray-effect mitigation techniques in two-dimensional x-y geometry. In particular, two angular finite element methods, and the modulated P1-equivalent S2 method, are analyzed. It is found that these techniques give varying levels of ray-effect mitigation on certain traditional test problems, but all of them yield discrete-ray solutions for a line source in a void. In general, it is shown that any transport angular discretization technique that results in a hyperbolic approximation for the directional gradient operator will yield a discrete-ray solution for a line source in a void. Since the directional gradient operator is in fact hyperbolic, it is not surprising that many discretizations of the operator retain this property. For instance, our results suggest that both continuous and discontinuous angular finite element methods produce hyperbolic approximations. Our main conclusion is that the effectiveness of any hyperbolic ray-effect mitigation technique will necessarily be highly problem dependent. In particular, such techniques must fail in problems that have the most severe ray effects, i.e., those that are “similar” to a line source in a void.

Space-Time Methods for Hyperbolic Conservation Laws

Two major challenges for computational fluid dynamics are problems that involve wave propagation over long times and problems with a wide range of amplitude scales. An example with both of these characteristics is the propagation and generation of acoustic waves, where the mean-flow amplitude scales are typically orders-of-magnitude larger than those of the generated acoustics. Other examples include vortex evolution and the direct simulation of turbulence. All of these problems require greater than second-order accuracy, whereas for nonlinear equations, most current methods are at best second-order accurate. Of the higher-order (greater than second-order) methods that do exist, most are tailored to high-spatial resolution, coupled with time integrators that are only second or third-order accurate. But for wave phenomena, time accuracy is as important as spatial accuracy.

A second order self-consistent IMEX method for radiation hydrodynamics

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.

Discontinuous Galerkin for Hyperbolic Systems with Stiff Relaxation

A Discontinuous Galerkin method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is unresolved, the method is accurate in the sense that it accurately represents the systems Chapman-Enskog approximation. Results are presented for the hyperbolic heat equation and coupled radiation-hydrodynamics.

Comoving-frame radiation transport for nonrelativistic fluid velocities

Abstract We investigate the comoving-frame treatment of radiation transport for use in problems of nonrelativistic radiation hydrodynamics. The transport equation is re-derived, to O(v/c), retaining a term that is traditionally omitted. This reduced equation is not just formally, but also physically, correct to O(v/c), inasmuch as it keeps the wave speed bounded by light speed and can transformed to the correct Eulerian-frame transport equation in any physical regime. We strongly recommend that this equation, and its moments, be used in all situations where the fluid-flow speeds are nonrelativistic.

Temporal Regularization of the

In this paper, we introduce a regularization of the

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equations for one-dimensional, slab geometries. These equations are used to describe particle transport through a material medium. Our regularization is based on a temporal splitting of fast and slow dynamics in the

Numerical analysis of time integration errors for nonequilibrium radiation diffusion

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