Enhanced Verification Test Suite for Physics Simulation Codes

Kamm, James R.; Brock, Jerry S.; Brandon, S.; Cotrell, David; Johnson, Bryan M.; Knupp, Patrick; Rider, William J.; Trucano, Timothy Guy; Weirs, V. Gregory

doi:10.2172/950084

Cited by 12 publications

(9 citation statements)

References 37 publications

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“…This parallels the manner other self-similar solutions (e.g. the Sedov–Taylor blast wave [20–22]) are used for code verification. A survey of the current literature indicates that there is a need for benchmarks for problems with radiation, electron and ion coupling: the extant solutions that exist are for infinite media [3,23] or shock waves without radiation effects [24].…”

Section: Introductionsupporting

confidence: 54%

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Bennett

McClarren

2021

Proc. R. Soc. A.

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We consider a non-equilibrium plasma radiatively heated by an external source in the high-energy density regime. It is shown that self-similar solutions resembling the classic Marshak wave exist for the ion and electron temperatures, if the electron–ion coupling coefficient scales inversely proportional to either the time from when the heating begins or to the square of the distance from the surface of the plasma. We discuss how such a coupling coefficient may arise, and demonstrate that these solutions are also useful for verifying simulation codes that treat radiation–electron–ion coupling in high-energy density plasmas.

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Section: Introductionsupporting

confidence: 54%

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Bennett

McClarren

2021

Proc. R. Soc. A.

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“…It consists in a cylindrical beryllium shell which collapses responding to an initial inwardly directed radial velocity field. The initial setup is taken from [92]. The shell Ω with inner radius Fig.…”

Section: Cylindrical Shell Compressionmentioning

confidence: 99%

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

Peshkov

Boscheri

Loubère

et al. 2019

Journal of Computational Physics

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The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences of the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.Keywords: symmetric hyperbolic thermodynamically compatible systems (SHTC), unified first order hyperbolic model of continuum mechanics, viscoplasticity and elastoplasticity, arbitrary high-order ADER Discontinuous Galerkin and Finite Volume schemes, path-conservative methods and stiff source terms, direct ALE exhibit properties of both elastic solids and viscous fluids [1; 2]. Such hydrodynamic-type effects in solids are naturally treated in the Eulerian settings. It is therefore important to have also a proper Eulerian formulation of solid mechanics, since it is more suitable for treating large deformations. Moreover, an Eulerian formulation is also required for moving mesh techniques based on the Arbitrary Lagrangian Eulerian formulation, see [19], for example.In contrast to the Lagrangian frame, in which the description of the dynamics of elastic and plastic solids always relies on the use of strain measures (e.g. deformation gradient) and therefore on a rigorous and objective geometric approach, there are historically two different possibilities to formulate the solid dynamics equations in the Eulerian frame: the hypoelastic and the hyperelastic one. In the hypoelastic-type models the stress tensor plays the role of the thermodynamic state variable along side with the mass, momentum and energy densities, and thus, an evolution equation for the stress tensor is employed (usually for its trace-less part). On the other hand, the hyperelastic Eulerian models, similar to their Lagrangian counterparts, rely on the use of a strain measure as the primary state variable. They are therefore also based on a rigorous geometric description of solid mechanics. The stress tensor in such models is considered merely as the constitutive momentum flux and should be computed from a stress-strain constitutive relation which is completely determined by defining the energy potential. The...

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“…This 2D problem was discussed by Taylor [98] and has been revisited since by many researchers since [35,34]. The problem is also discussed in [54]. The problem is of particular interest because it represents a vortical flow problem for which there is a known solution.…”

Section: Taylor-green Vortexmentioning

confidence: 99%

Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)

Burton

Morgan

Carney

et al. 2015

Journal of Computational Physics

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This work presents an extension of a second order cell-centered hydrodynamics scheme on unstructured polyhedral cells [13] toward higher order. The goal is to reduce dissipation, especially for smooth flows. This is accomplished by multiple piecewise linear reconstructions of conserved quantities within the cell. The reconstruction is based upon gradients that are calculated at the nodes, a procedure that avoids the least-square solution of a large equation set for polynomial coefficients. Conservation and monotonicity are guaranteed by adjusting the gradients within each cell corner. Results are presented for a wide variety of test problems involving smooth and shock-dominated flows, fluids and solids, 2D and 3D configurations, as well as Lagrange, Eulerian, and ALE methods. stress and momentum are solved on offset control volumes such that the logical center of each lies on the boundary of the other. Cell-centered hydrodynamics schemes (CCH) in which all conservation equations are solved on a common control volume have been widely applied to Eulerian methods, but only recently widely applied to Lagrange. A cell-centered Lagrange method was first suggested by Godunov [49,48]. Early implementations such as that in the CAVEAT code [2,39] solved an approximate Riemann problem at cell faces rather than at the nodes. It was not until the seminal work of Després and Mazeran [33] that a solution at the nodes was found. Since then, interest in CCH methods has increased and at least three additional formulations have arisen [74,3,13] giving rise to extensions in many areas [25,32,58,75,76,71,77,70,46,45,73,72,21,14,81,15,80]. Although the discussion in this paper is centered about the CCH2 formulation of [13,15], it is relevant to all.We begin with an overview of the CCH2 method. Details are in the cited references that we summarize here in very general terms. Reference [13] describes the basic XY formulation while [15] describes an RZ formulation based on conservative fluxes that preserves symmetry on equiangular polar meshes. The cyclic ordering of the steps depends upon the particular implementation. For purposes of discussion, we begin with the finite volume integration.Finite volume integration. The extensive evolution or rate equations for momentum, deformation, and total energy are expressed as surface integralsUin which M z is the cell mass and {u z ,γ z ,τ z } are respectively specific cell average rates of change of velocity, deformation, and total energy. The fundamental challenge in CCH is the determination of the surface fluxes u p and σ p that are solutions to a Riemann problem. The decomposition of the total energy into kinetic and internal rates k z ,ė z will be discussed later in Section 2.1. A stress rateσ z is derived from the internal energy rate and deformation rate through a constitutive model such as that described in Appendix A. The rate equations are integrated to yield new values for velocity, stress, and total energy.Conservative reconstruction. The finite volume method provides no direct infor...

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Enhanced Verification Test Suite for Physics Simulation Codes

Cited by 12 publications

References 37 publications

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)

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