Early development of implicit methods for Computational Fluid Dynamics at NASA Ames

Pulliam, Thomas H.

doi:10.1016/j.compfluid.2008.06.012

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…For example, his coding style dominated Ames-developed codes. A comprehensive review, including Steger's contributions on Ames implicit algorithm development is given by Pulliam (2009).…”

Section: Overflowmentioning

confidence: 99%

CFD technology development at NASA Ames - A mission computing perspective

Kwak

Kiris

2016

Mechanical Engineering Reviews

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“…For example, his coding style dominated Ames-developed codes. A comprehensive review, including Steger's contributions on Ames implicit algorithm development is given by Pulliam (2009).…”

Section: Overflowmentioning

confidence: 99%

CFD technology development at NASA Ames - A mission computing perspective

Kwak

Kiris

2016

Mechanical Engineering Reviews

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“…Numerical approximations of the steady solution of the Euler equations is a long lasting activity in computational physics since the 70's, see [12]. It has led to the development of a tremendous amount of techniques over the years, for instance the implicit time algorithm [1] with high-order finite difference methods [2] or some of the first simulations for two-and three-dimensional complex geometries calculated on Illiac IV Computer [17,14,13].…”

Section: Introductionmentioning

confidence: 99%

a posteriori stabilized sixth-order finite volume scheme with adaptive stencil construction -- Basics for the 1D steady-state hyperbolic equations

Machado¹,

Clain²,

Loubère³

2021

Preprint

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We propose an adaptive stencil construction for high order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation. The stencil is shifted away from troubles (shocks, discontinuities, etc.) leading to less oscillating polynomial reconstructions. Experimented on linear, Bürgers', and Euler equations, we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations. Moreover we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

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a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

2017

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To cite this version:Stéphane Clain, Raphaël Loubère, Gaspar Machado. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations. 2016. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equationsWe propose a new family of finite volume high-accurate numerical schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which control the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a chain detector to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers', and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations.

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Early development of implicit methods for Computational Fluid Dynamics at NASA Ames

Cited by 8 publications

References 22 publications

CFD technology development at NASA Ames - A mission computing perspective

CFD technology development at NASA Ames - A mission computing perspective

a posteriori stabilized sixth-order finite volume scheme with adaptive stencil construction -- Basics for the 1D steady-state hyperbolic equations

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

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