Cancellation problem of preconditioning method at low Mach numbers

Lee, Sang-Hyeon

doi:10.1016/j.jcp.2007.04.001

Cited by 23 publications

(10 citation statements)

References 21 publications

(27 reference statements)

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“…3(c) provides a typical picture of checkerboard decoupling obtained by All-Speed-Roe scheme with the construction of Eqs. (8), (16), (17) and (18). It is obvious that traditional preconditioned Roe scheme is much better than All-Speed-Roe scheme in avoiding the checkerboard decoupling.…”

Section: Numerical Experimentsmentioning

confidence: 99%

An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour

2008

Journal of Computational Physics

123

145

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Section: Numerical Experimentsmentioning

confidence: 99%

An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour

2008

Journal of Computational Physics

123

145

View full text Add to dashboard Cite

“…The non-dimensional conservative form of preconditioned governing equations (for inviscid and laminar cases) in vector form are written as follows [18,49,50]:…”

Section: Preconditioning Governing Equationsmentioning

confidence: 99%

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Esfahanian

Akbarzadeh

Hejranfar

2010

Numerical Methods in Fluids

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SUMMARYAn improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet-cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow-field by a power-law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell-centered Jameson's finite volume algorithm. The stabilization is achieved via the second-and fourth-order artificial dissipation scheme. Explicit four-step Runge-Kutta time integration is applied to achieve the steady-state condition. Results presented in the paper focus on the pressure distribution on hydrofoils wall, velocity profiles, lift and drag forces, length of sheet cavitation, and effect of the power-law preconditioning method on convergence speed. The results show satisfactory agreement with numerical and experimental works of others. The scheme has a progressive effect on the convergence speed. The results indicate that using the power-law preconditioner improves the convergence rate, significantly.

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“…In a steady state, the solution of the modi fied (preconditioned) system coincides with that of the original system of equations. An unsteady solution is found by applying dual time stepping [24].…”

Section: Introductionmentioning

confidence: 99%

Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers

Волков

Karpenko

2015

Comput. Math. and Math. Phys.

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Abstract-Features of the simulation of low velocity inviscid and viscous compressible gas flows are considered, and a finite volume discretization of gas dynamics equations at low Mach numbers on unstructured meshes is discussed. Preconditioning based on the use of physical variables is used to speed up the convergence of time marching to a steady state and to improve the accuracy of the steady state solution. The structure of the preconditioning matrix and the diagonalization of the Jacobian of the preconditioned system of equations are discussed. The capabilities of this approach are demon strated using model gasdynamic simulations in a wide range of Mach numbers.

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Cancellation problem of preconditioning method at low Mach numbers

Cited by 23 publications

References 21 publications

An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour

An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers

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