Numerical simulation of shock wave interactions with channel bends and gas nonuniformities

Fursenko, A. A.; Sharov, Dmitri; Timofeev, Edward N.; Voinovich, P. A.

doi:10.1016/0045-7930(92)90046-x

Cited by 14 publications

(14 citation statements)

References 6 publications

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“…The quantities u g j , U f + l , j , u%, uZm+ 1, i = 0, 1 ,..., n + 1, j = 0, 1, ..., rn +1, CY = 1,2 are assumed to be known. Let us consider two schemes for (15): a certain alternating direction scheme and the completely implicit scheme in which all the terms in the right-hand side of (15) are taken from the upper time layer. The first scheme is economical, but one cannot answer the question both on its monotony or even on its stability.…”

Section: Viscosity In Momentum Equationsmentioning

confidence: 99%

Compound difference schemes for time‐dependent equations on non‐uniform nets

Charakhch’yan

1994

Commun. Numer. Meth. Engng.

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SUMMARYA new approach to constructing monotonous seoond-order-accurate schemes for time-dependent Navier-Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with 'viscous' terms. The method is illustrated by the problem on compression of deuterium in a conical solid-body target with viscous heating of deuterium.

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Section: Viscosity In Momentum Equationsmentioning

confidence: 99%

Compound difference schemes for time‐dependent equations on non‐uniform nets

Charakhch’yan

1994

Commun. Numer. Meth. Engng.

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“…Subsequent work by Colella and Glaz [6] as well as Colella and Henderson [7] considered the application of patch-based mesh adaptation techniques on a Cartesian mesh with localized mesh refinement in designated regions of the flow field. Shortly thereafter, other possibly more general solution-directed adaptive mesh refinement (AMR) schemes were proposed and developed by Fursenko, Timofeev, Voinovich and co-researchers [8][9][10][11][12], Sun and Takayama [13] and Henderson et al [14] for compressible, inviscid, unsteady flow applications dealing with shock waves and their complex interactions.…”

Section: Introductionmentioning

confidence: 99%

Parallel implicit anisotropic block-based adaptive mesh refinement finite-volume scheme for the study of fully resolved oblique shock wave reflections

2015

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A new parallel, fully implicit, anisotropic blockbased adaptive mesh refinement (AMR) finite-volume scheme is proposed, described and demonstrated for the prediction of laminar, compressible, viscous flows associated with unsteady oblique shock reflection processes. The proposed finite-volume method provides numerical solutions to the Navier-Stokes equations governing the flow of polytropic gases in an accurate and efficient manner on twodimensional, body-fitted, multi-block meshes consisting of quadrilateral computational cells. The combination of the anisotropic AMR and parallel implicit time-marching techniques adopted is shown to readily facilitate the simulation of challenging and complex shock interaction problems, as represented by the time-accurate predictions of unsteady oblique shock reflection configurations with fully resolved internal shock structures.Keywords Oblique shock reflections · Parallel implicit finite-volume methods · Anisotropic adaptive mesh refinement (AMR) · Newton-Krylov-Schwarz (NKS)

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“…This scheme is based on the TVD approach combined with second-order upwind dilferences and a solution of the Riemann problem to obtain inter-zone fluxes. A more detailed description of the numerical method used in the Euler code can be found in [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…An unstructured grid Euler solver [9][10][11][12] with a local refinement based on a density gradient is used in this research. Its advantage is an automatic capture of thin regions of induced vorticity at the VDI boundary.…”

Section: Introductionmentioning

confidence: 99%