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Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
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TLDR
In this paper, a higher order numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretisation.Abstract:
A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problemsread more
Citations
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A fourth-order-accurate finite volume compact method for the incompressible Navier-Stokes solutions
TL;DR: A finite volume fourth-order-accurate compact scheme for discretization of the incompressible Navier–Stokes equations in primitive variable formulation is presented.
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Compact reconstruction schemes with weighted eno limiting for hyperbolic conservation laws
Debojyoti Ghosh,James D. Baeder +1 more
TL;DR: A class of compact-reconstruction weighted essentially non-oscillatory CRWENO schemes is presented in this paper where lower order compact stencils are identified at each interface and combined using the WENO weights, which yields a higher order compact scheme for smooth solu- tions with superior resolution and lower truncation errors, compared to the W ENO schemes.
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An efficient high-order algorithm for solving systems of reaction-diffusion equations
TL;DR: An efficient higher‐order finite difference algorithm is presented in this article for solving systems of two‐dimensional reaction‐diffusion equations with nonlinear reaction terms with high‐order accuracy in the spatial and temporal dimensions.
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Compact fourth-order finite volume method for numerical solutions of Navier-Stokes equations on staggered grids
Arpiruk Hokpunna,Michael Manhart +1 more
TL;DR: A higher-order divergence-free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes.
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Literature Survey of Numerical Heat Transfer (2000–2009): Part II
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.
References
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Compact finite difference schemes with spectral-like resolution
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.
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A second-order projection method for the incompressible navier-stokes equations
TL;DR: In this paper, a second-order projection method for the Navier-Stokes equations is proposed, which uses a specialized higher-order Godunov method for differencing the nonlinear convective terms.
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Low-storage Runge-Kutta schemes
TL;DR: All second-order, many third- order, and a few fourth-order Runge-Kutta schemes can be arranged to require only two storage locations per variable, compared with three needed by Gill's method.
Low-dissipation and -dispersion Runge-Kutta schemes for computational acoustics
TL;DR: It is shown that if the traditional Runge?Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than those allowed by the stability limit are necessary.
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Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics
TL;DR: In this paper, the authors investigated accurate and efficient time advancing methods for computational acoustics, where nondissipative and nondispersive properties are of critical importance, and proposed low-dissipation and low-dispersion Runge?Kutta (LDDRK) schemes, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation.