Generalized Noh self-similar solutions of the compressible Euler equations for hydrocode verification

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.

doi:10.1016/j.jcp.2018.07.054

Cited by 10 publications

(6 citation statements)

References 25 publications

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“…These solutions did not attract attention until they were rediscovered by Noh (1983Noh ( , 1987 for a particular case of ideal-gas EoS and strong accretion shocks. Due to the simplicity of the Noh problem formulation and the explicit analytic form of its solution, it became the workhorse of compressible hydrocode verification for over three decades; see Velikovich, Giuliani & Zalesak (2018) and references therein. Hereafter, this particular case will be called the classic Noh solution.…”

Section: Introductionmentioning

confidence: 99%

Stability of expanding accretion shocks for an arbitrary equation of state

et al. 2021

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We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

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Section: Introductionmentioning

confidence: 99%

Stability of expanding accretion shocks for an arbitrary equation of state

et al. 2021

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“…His self-similar problem is designed to focus on the excess heating that occurs when a shock is reflected off a wall in plane symmetry or from a point of convergence in cylindrical or spherical symmetry. The Noh problem is widely used for code verification [54,70].…”

Section: John Von Neumann: the 1950 Journal Article By Vonmentioning

confidence: 99%

Artificial Viscosity -- Then and Now

Margolin¹,

Lloyd‐Ronning²

2022

Preprint

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In this paper, we recount the history of artificial viscosity, beginning with its origin in previously unpublished and unavailable documents, continuing on to current research and ending with recent work describing its physical basis that suggests new directions for improvement. We focus on the underlying ideas that recognize the finiteness of scale and of measurement. Los Alamos report LA-UR-22-20270Keywords Shocks • Artificial Viscosity • Finite Scale Theory Preface "We don't see things as they are; we see them as we are." (Anonymous)We celebrate the centennial anniversary of Richard Becker's seminal paper on shock structure [4]. Becker's paper is most often cited for his clever solution of the Navier-Stokes equations for the planar shock. However Becker's main purpose was to cast doubt on the ability of the Navier-Stokes equations to model shock structure. Becker concluded from his solution that a shock would be about one molecular mean free path wide, violating the assumptions under which the Navier-Stokes equations are derived from the Boltzmann equation [24].

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“…Scale invariant/self-similar solutions of the Euler equations are broadly used, as seen in [51]. Exhaustive discussions of their self-similar behavior can be found in the well-known works of Sedov [52], Olver [53], and many others.…”

Section: Self-similarity and Scalingmentioning

confidence: 99%

Self-similar diffuse boundary method for phase boundary driven flow

Schmidt,

Quinlan,

Runnels

2022

Preprint

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Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid-fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid-fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid-fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. These demonstrate expected behavior in all cases. Convergence analysis is also performed and compared against the sharp-interface solution, and linear convergence is observed. This method lays the groundwork for the extension to viscous flow, and the solution of problems involving time-varying mass-flux boundaries.

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Generalized Noh self-similar solutions of the compressible Euler equations for hydrocode verification

Cited by 10 publications

References 25 publications

Stability of expanding accretion shocks for an arbitrary equation of state

Stability of expanding accretion shocks for an arbitrary equation of state

Artificial Viscosity -- Then and Now

Self-similar diffuse boundary method for phase boundary driven flow

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