Multidimensional Dissipation for Upwind Schemes: Stability and Applications to Gas Dynamics

Sanders, Richard; Morano, E.; Druguet, Marie-Claude

doi:10.1006/jcph.1998.6047

Cited by 180 publications

(148 citation statements)

References 16 publications

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“…(16) to all characteristic fields and evaluating η in a multi-dimensional way. In all our computations we have successfully utilised the "H-correction" by Sanders et al [26] for this purpose. For instance in the x 2 -direction it takes the formη j,k+…”

Section: Approximate Riemann Solver Methodsmentioning

confidence: 99%

A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains

Deiterding

2009

Computers & Structures

125

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An adaptive finite volume approach is presented to accurately simulate shockinduced combustion phenomena in gases, particularly detonation waves. The method uses a Cartesian mesh that is dynamically adapted to embedded geometries and flow features by using regular refinement patches. The discretisation is a reliable linearised Riemann solver for thermally perfect gas mixtures; detailed kinetics are considered in an operator splitting approach. Besides easily reproducible ignition problems, the capabilities of the method and its parallel implementation are quantified and demonstrated for fully resolved triple point structure investigations of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures in two and three space dimensions.

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Section: Approximate Riemann Solver Methodsmentioning

confidence: 99%

A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains

Deiterding

2009

Computers & Structures

125

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“…The effect of different numerics on Navier-Stokes computations of hypersonic shock/boundary-layer interaction flows on a 25-55 • double-cone configuration was studied by Druguet, Candler and Nompelis (2005) by implementing different flux schemes to calculate the inviscid terms. It was observed that the modified Steger-Warming scheme gives results that are as accurate as, and is as attractive as, other wellknown high-quality, more sophisticated schemes, such as the Roe scheme with the van Leer slope limiter (Sanders, Morano & Druguet, 1998). It was found that, when the grid is fine enough, all of the flux evaluation schemes give the same results, though this may require a very large number of points for the most dissipative schemes such as the original SWFS.…”

Section: Simulation Methodologymentioning

confidence: 98%

Numerical prediction of shock/boundary-layer interactions at high Mach numbers using a modified Spalart–Allmaras model

Pasha

Juhany

Khalid

2018

Engineering Applications of Computational Fluid Mechanics

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The Reynolds-averaged Navier-Stokes equations with one-equation turbulence models are used to simulate the flow field past a cone-flare geometry in the Mach number range from 5 to 8 with emphasis on the interaction region of the flare shock with the upstream boundary layer. A model based on the physics of shock unsteadiness is used to correct the standard Spalart-Allmaras turbulence model to improve the prediction of the extent of the separation bubble arising from the shock/turbulent boundary-layer interaction and its accompanying peak pressure and aerothermal loads on the surface. The computed results are validated against the experimental data. The limitations of the shock-unsteadiness model and the extent of the improvement in predicting the heat flux are discussed. ARTICLE HISTORY

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“…It is said that the numerical instability is mainly due to the choice of Roe speed. The detailed introductions for the numerical instabilities of upwind schemes are referred to [20] [21] [22]. In order to eliminate such kind of instabilities, the H-correction procedure in [21] is taken to solve these flaws.…”

Section: The Nonlinear Equationsmentioning

confidence: 99%

Conservative and Easily Implemented Finite Volume Semi-Lagrangian WENO Methods for 1D and 2D Hyperbolic Conservation Laws

Hu¹

2017

JAMP

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The paper is devised to propose finite volume semi-Lagrange scheme for approximating linear and nonlinear hyperbolic conservation laws. Based on the idea of semi-Lagrangian scheme, we transform the integration of flux in time into the integration in space. Compared with the traditional semi-Lagrange scheme, the scheme devised here tries to directly evaluate the average fluxes along cell edges. It is this difference that makes the scheme in this paper simple to implement and easily extend to nonlinear cases. The procedure of evaluation of the average fluxes only depends on the high-order spatial interpolation. Hence the scheme can be implemented as long as the spatial interpolation is available, and no additional temporal discretization is needed. In this paper, the high-order spatial discretization is chosen to be the classical 5th-order weighted essentially non-oscillatory spatial interpolation. In the end, 1D and 2D numerical results show that this method is rather robust. In addition, to exhibit the numerical resolution and efficiency of the proposed scheme, the numerical solutions of the classical 5th-order WENO scheme combined with the 3rd-order Runge-Kutta temporal discretization (WENOJS) are chosen as the reference. We find that the scheme proposed in the paper generates comparable solutions with that of WENOJS, but with less CPU time.

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Multidimensional Dissipation for Upwind Schemes: Stability and Applications to Gas Dynamics

Cited by 180 publications

References 16 publications

A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains

A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains

Numerical prediction of shock/boundary-layer interactions at high Mach numbers using a modified Spalart–Allmaras model

Conservative and Easily Implemented Finite Volume Semi-Lagrangian WENO Methods for 1D and 2D Hyperbolic Conservation Laws

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