Implicit weighted essentially non-oscillatory schemes for the incompressible Navier-Stokes equations

Chen, Yih‐Nan; Yang, Shih-Chang; Yang, James

doi:10.1002/(sici)1097-0363(19991030)31:4<747::aid-fld901>3.0.co;2-f

Cited by 44 publications

(48 citation statements)

References 34 publications

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“…According to the analysis conducted by Turkel [15], the optimal value of α is 2.0. α=0.0, 1.0, 2.0, 3.0, and 4.0 are tested in the present paper. α=0.0, which means the precondition is not effective, is the mostly tested case in literatures [11][12][13][14]. For this case, the performance of the method is affected mainly by the pseudo-compressibility factor β.…”

Section: Parameters Selection Criterion For the Numerical Schemementioning

confidence: 97%

“…[12] using the third-and fifth-order upwind schemes, ref. [14] using the WENO scheme, ref. [23] using the second-and forth-order compact schemes and the experimental results [24][25][26].…”

Section: Applications To Unsteady Viscous Flowsmentioning

confidence: 99%

“…Rogers [12,13] proposed afterward the upwind schemes similar to compressible flow simulations to compute the incompressible flows. The high order WENO scheme was also employed by Chen [14] to solve the pseudo-compressible Navier-Stokes equations. The precondition concept imposed on the incompressible flow simulation, on the other hand, was proposed by Turkel [15].…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [11][12][13][14] cited above merely investigated the effects of the pseudo-compressibility factor against the convergence performance of the numerical schemes, and left the coupling effects with the preconditioning factor behind. Liu [16] and Esfahanian [17] applied Turkel's preconditioning technique in their computations.…”

Section: Introductionmentioning

confidence: 99%

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Preconditioned pseudo-compressibility methods for incompressible Navier-Stokes equations

Qian

Zhang

2010

Sci. China Phys. Mech. Astron.

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This paper investigates the pseudo-compressibility method for the incompressible Navier-Stokes equations and the preconditioning technique for accelerating the time marching for stiff hyperbolic equations, and derives and presents the eigenvalues and eigenvectors of the Jacobian matrix of the preconditioned pseudo-compressible Navier-Stokes equations in generally cur-vilinear coordinates. Based on the finite difference discretization the cored for efficiently solving incompressible flows numerically is established. The reliability of the procedures is demonstrated by the application to the inviscid flow past a circular cylinder, the laminar flow over a flat plate, and steady low Reynolds number viscous incompressible flows past a circular cylinder. It is found that the solutions to the present algorithm are in good agreement with the exact solutions or experimental data. The effects of the pseudo-compressibility factor and the parameter brought by preconditioning in convergence characteristics of the solution are investigated systematically. The results show that the upwind Roe's scheme is superior to the second order central scheme, that the convergence rate of the pseudo-compressibility method can be effectively improved by preconditioning and that the self-adaptive pseudo-compressibility factor can modify the numerical convergence rate significantly compared to the constant form, without doing artificial tuning depending on the specific flow conditions. Further validation is also performed by numerical simulations of unsteady low Reynolds number viscous incompressible flows past a circular cylinder. The results are also found in good agreement with the existing numerical results or experimental data. pseudo-compressibility method, preconditioning, upwind scheme, incompressible flow, Navier-Stokes equations

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Section: Parameters Selection Criterion For the Numerical Schemementioning

confidence: 97%

“…[12] using the third-and fifth-order upwind schemes, ref. [14] using the WENO scheme, ref. [23] using the second-and forth-order compact schemes and the experimental results [24][25][26].…”

Section: Applications To Unsteady Viscous Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Preconditioned pseudo-compressibility methods for incompressible Navier-Stokes equations

Qian

Zhang

2010

Sci. China Phys. Mech. Astron.

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“…Various schemes [1,[4][5][6][7]11,14,15,17,21,23,29] have been proposed in the near past to solve the N-S equations both in the primitive variable (Eqs. (1)-(3)) and the .…”

Section: Introductionmentioning

confidence: 99%

An efficient transient Navier–Stokes solver on compact nonuniform space grids

Kalita

Dass

Nidhi

2008

Journal of Computational and Applied Mathematics

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In this paper, we propose an implicit higher-order compact (HOC) finite difference scheme for solving the two-dimensional (2D) unsteady Navier-Stokes (N-S) equations on nonuniform space grids. This temporally second-order accurate scheme which requires no transformation from the physical to the computational plane is at least third-order accurate in space, which has been demonstrated with numerical experiments. It efficiently captures both transient and steady-state solutions of the N-S equations with Dirichlet as well as Neumann boundary conditions. The proposed scheme is likely to be very useful for the computation of transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation. Numerical results are presented and compared with analytical as well as established numerical data. Excellent comparison is obtained in all the cases.

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Applications of the artificial compressibility method for turbulent open channel flows

Lee

Teubner

Nixon

et al. 2006

Numerical Methods in Fluids

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SUMMARYA three-dimensional (3-D) numerical method for solving the Navier-Stokes equations with a standard k-turbulence model is presented. In order to couple pressure with velocity directly, the pressure is divided into hydrostatic and hydrodynamic parts and the artiÿcial compressibility method (ACM) is employed for the hydrodynamic pressure. By introducing a pseudo-time derivative of the hydrodynamic pressure into the continuity equation, the incompressible Navier-Stokes equations are changed from elliptic-parabolic to hyperbolic-parabolic equations. In this paper, a third-order monotone upstreamcentred scheme for conservation laws (MUSCL) method is used for the hyperbolic equations. A system of discrete equations is solved implicitly using the lower-upper symmetric Gauss-Seidel (LU-SGS) method. This newly developed numerical method is validated against experimental data with good agreement.

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Implicit weighted essentially non-oscillatory schemes for the incompressible Navier-Stokes equations

Cited by 44 publications

References 34 publications

Preconditioned pseudo-compressibility methods for incompressible Navier-Stokes equations

Preconditioned pseudo-compressibility methods for incompressible Navier-Stokes equations

An efficient transient Navier–Stokes solver on compact nonuniform space grids

Applications of the artificial compressibility method for turbulent open channel flows

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