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Journal ArticleDOI

A Novel Semi-Explicit Spatially Fourth Order Accurate Projection Method for Unsteady Incompressible Viscous Flows

07 Dec 2009-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 56, Iss: 8, pp 665-684
TL;DR: In this paper, a compact higher order finite-difference based numerical solution technique to the primitive variable formulation of unsteady incompressible Navier Stokes equations (UINSE) on staggered grids is described.
Abstract: This article describes a simple and elegant compact higher order finite-difference based numerical solution technique to the primitive variable formulation of unsteady incompressible Navier Stokes equations (UINSE) on staggered grids. The method exploits the advantages of the D'yakanov ADI-like scheme and a non-iterative pressure correction based fractional step method. Spatial derivatives are discretized to fourth order accuracy and the time integration is realized through the Euler explicit method. The fast and efficient iterative solution to the discretized momentum and pressure Poisson equations is achieved using a variant of conjugate gradient method. Spatial accuracy and robustness of the solver are tested through its application to relevant benchmark problems.

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Citations
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Journal ArticleDOI
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

58 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed two-dimensional fast fluid dynamics (2-D FFD) into three-dimensional FFD (3-D FDFD) for real-time indoor air-flow simulations.
Abstract: Fast fluid dynamics (FFD) can potentially be used for real-time indoor air-flow simulations This study developed two-dimensional fast fluid dynamics (2-D FFD) into three-dimensional fast fluid dynamics (3-D FFD) The implementation of boundary conditions at the outlet was improved with a local mass conservation method A near-wall treatment for the semi-Lagrangian scheme was also proposed This study validated the 3-D FFD with five flows that have features of indoor air flow The results show that the 3-D FFD can successfully capture the three dimensionality of air-flow and provide reliable and reasonably accurate simulations for indoor air flows with a speed of about 15 times faster than current computational fluid dynamics (CFD) tools

38 citations

Journal ArticleDOI
TL;DR: In this paper, a new family of fourth-order compact difference schemes for the three-dimensional semilinear convection-diffusion equation with variable coefficients is presented, combining with the Simpson integral formula and parabolic interpolation, four-order schemes are derived based on two different types of dual partitions.
Abstract: In this article, a new family of fourth-order compact difference schemes for the three-dimensional semilinear convection-diffusion equation with variable coefficients is presented. Like the finite-volume method, a dual partition is introduced. Combining with the Simpson integral formula and parabolic interpolation, fourth-order schemes are derived based on two different types of dual partitions. Moreover, a sixth-order finite-difference discretization strategy is developed, which is based on the fourth-order compact discretization and Richardson extrapolation technique. This extrapolation technique can achieve a sixth-order-accurate solution on fine grids directly, without the need for interpolation. Numerical experiments are conducted to verify the feasibility of this new method and the high accuracy of these fourth-order schemes and extrapolation formulas.

23 citations

Journal ArticleDOI
TL;DR: A new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid, which shows uniform order of accuracy, both in space and time.

12 citations

01 Nov 1997
TL;DR: The proposed schemes appear to be attractive alternatives to the standard Pade schemes for computations of the Navier?Stokes equations.
Abstract: This paper presents a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric and may be considered a more general version of the standard compact (Pade) schemes discussed by Lele. They are different from the standard Pade schemes, in that the first and second derivatives are evaluated simultaneously. For the same stencil width, the proposed schemes are two orders higher in accuracy, and have significantly better spectral representation. Eigenvalue analysis, and numerical solutions of the one-dimensional advection equation are used to demonstrate the numerical stability of the schemes. The computational cost of computing both derivatives is assessed and shown to be essentially the same as the standard Pade schemes. The proposed schemes appear to be attractive alternatives to the standard Pade schemes for computations of the Navier?Stokes equations.

10 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a higher-order compact scheme that is O(h4) on the nine-point 2D stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations.
Abstract: A higher-order compact scheme that is O(h4) on the nine-point 2-D stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations. The resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software. We also show that special treatment of the wall boundary conditions is required. The method is tested on representative model problems and compares very favourably with other schemes in the literature.

239 citations

Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations were approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points, and the key advantage of the new compact 4-order scheme is that it allows direct iteration for low-to-mediwn Reynolds numbers.
Abstract: SUMMARY We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re $1500 point-SOR iteration is used and the convergence is fast.

238 citations

Journal ArticleDOI
TL;DR: In this article, central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space, numerical stability and dispersion relation preservation, and some well-known compact schemes that were found to be G-K-S and time stable are shown to be unstable for selective length scales by this analysis.

177 citations


"A Novel Semi-Explicit Spatially Fou..." refers background in this paper

  • ...In the case of numerical simulation of wave propagation or acoustic problems, the higher order upwind schemes are indispensable [18, 19, 22]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a family of finite difference schemes for the first and second derivatives of smooth functions is presented, which are Hermitian and symmetric and may be considered a more general version of the standard compact (Pade) schemes discussed by Lele.

152 citations

Journal ArticleDOI
TL;DR: Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy.
Abstract: SUMMARY A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601×601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.

136 citations