The calculation of the interaction of non-stationary shock waves and obstacles

Rusanov, V. V.

doi:10.1016/0041-5553(62)90062-9

Cited by 496 publications

(459 citation statements)

References 3 publications

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“…The pressure is then computed iteratively by solving an elliptic equation, and the velocity components are projected onto the divergence-free space, thus recovering the incompressible sought solution. The advective fluxes are discretised by the Rusanov flux (Rusanov 1961;Drikakis and Rider 2004), and similar to the compressible case the fifth-order MUSCL scheme has been used for reconstructing the cell-face variables. For the time integration, a second-order Runge-Kutta method in its Strong-Stability-Preserving version (Spiteri and Ruuth 2002), has been employed in conjunction with CFL numbers of 0.2 and 0.5 for the incompressible and compressible solvers, respectively.…”

Section: Methodsmentioning

confidence: 99%

Computing multi-mode shock-induced compressible turbulent mixing at late times

et al. 2015

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Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long enough times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late time behaviour of single-shocked Richtmyer-Meshkov Instability (RMI) and associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible-incompressible solver that removes the low-Mach number limitations of the compressible solvers, thus allowing numerical simulations of late time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

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Section: Methodsmentioning

confidence: 99%

Computing multi-mode shock-induced compressible turbulent mixing at late times

et al. 2015

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“…The flux polynomial in each element is extrapolated to the interfaces, giving left and right flux states f L and f R on each side of the interface. A common numerical flux f * is found at each interface using an approximate Riemann solver such as the Rusanov [43] or Roe method [30] for the inviscid flux and the LDG method [44] for the viscous flux. The next step is to construct a globally continuous flux polynomial.…”

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confidence: 99%

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

Bull

Jameson

2015

AIAA Journal

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“…They clearly reveal the emergence of a liquid column bounded by two closely spaced shocks, giving us confidence that we are witnessing the birth of what would become a delta-shock in the limit as F → ∞. For finite F , the shallow water equations (1.1), (1.2) remain non-degenerate as a hyperbolic system and the numerical solutions were obtained using finite volume techniques for hyperbolic systems, the local LaxFriedrichs or Rusanov (1961) scheme, and its second order extension by Kurganov & Tadmor (2000). Neither scheme requires the solution of the Riemann problem, only the determination of the fluxes as functions of the conserved variables η and ηu, and a bound on the maximum wave speed, taken as |u| + √ η/F .…”

Section: Introductionmentioning

confidence: 94%

Non-classical shallow water flows

Edwards¹,

Howison²,

Ockendon³

et al. 2007

IMA Journal of Applied Mathematics

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This paper deals with violent discontinuities in shallow water flows with large Froude number F .On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity may be described by a delta-shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step function components. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted.For flows on a sloping base, we show that for flow with an aspect ratio of O(F −2 ) on a base with an O(1) or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a deltashock. The physical manifestation of this discontinuity is a small 'tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base.

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The calculation of the interaction of non-stationary shock waves and obstacles

Cited by 496 publications

References 3 publications

Computing multi-mode shock-induced compressible turbulent mixing at late times

Computing multi-mode shock-induced compressible turbulent mixing at late times

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

Non-classical shallow water flows

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