Analysis of central and upwind compact schemes

Sengupta, Tapan K.; Ganeriwal, G.; De, S. K.

doi:10.1016/j.jcp.2003.07.015

Cited by 169 publications

(223 citation statements)

References 25 publications

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“…Compact Scheme (OUCS3) [29,37] is used to discretize the nonlinear convection terms in Eq. (4), for its spectrallike accuracy.…”

Section: Numerical Methods and Filtersmentioning

confidence: 99%

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

Bagade¹,

Krishnan²,

Sengupta³

2015

FAE

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Here, Direct Numerical Simulation (DNS) of low Reynolds number (Re) flow in the presence of free stream turbulence (FST) pertaining to micro-aerial vehicle (MAV) is reported. The focus is on numerically simulating the flow around an airfoil at low Re to understand its behaviour using high accuracy compact schemes (T. K. Sengupta, High Accuracy Computing Methods, Cambridge University Press, New York, 2013.) [1]. In low Re aerodynamics, the flow is characterized by unsteady separation bubbles and vortex shedding from the suction surface and the trailing edge as well, which make it different from high Re aerodynamics. The maximum attainable lift coefficient and lift-to-drag ratio decreases drastically at low Re, as compared to high Re flows. Such flows are also important because of their susceptibility to background disturbances. Stalling of aircraft wing is one such phenomenon where free stream turbulence (FST) plays a crucial role. In this work, effects of FST, effects of Re and angles of attack  are studied with respect to flow separation and vortex shedding. Flow characterization is done for the AG24 airfoil, at Re =60,000 and 400,000, with and without consideration of FST in the range of angles of attack, 6 6The computational results are compared with the experimental results of Williamson et al. ( Summary of Low Speed Airfoil Data, volume 5, Dept. of Aerospace Engineering, UIUC, 2007 ) [2] and are found to be in good agreement. Flow simulation over AG24 airfoil is performed here via parallel computation, using high accuracy compact schemes for spatial discretization and optimized Runge-Kutta (ORK4) scheme for time marching [1]. This paper also discusses proper implementation of filters and FST model.

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“…Compact Scheme (OUCS3) [29,37] is used to discretize the nonlinear convection terms in Eq. (4), for its spectrallike accuracy.…”

Section: Numerical Methods and Filtersmentioning

confidence: 99%

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

Bagade¹,

Krishnan²,

Sengupta³

2015

FAE

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“…It is, thus, desirable that the right-hand side of (10) is made to have nearly the same Fourier transform in space as the original partial derivative shown in the left-hand side of (10). Within the DRP analysis framework [8,18], which has been applied with great success to approximate / x in the one-dimensional context, define first the Fourier transform and its inverse for /ðx; yÞ in two space dimensions as follows: In approximation sense, the effective wave number e a a in e a a ¼ ðe a a; e b bÞ can be regarded as the right-hand side of (25) …”

Section: Dispersion Relation-preserving Convection Schemementioning

confidence: 99%

Development of a Dispersion Relation-Preserving Upwinding Scheme for Incompressible Navier–Stokes Equations on NonStaggered Grids

Chiu

Sheu

Lin

2005

Numerical Heat Transfer, Part B: Fundamentals

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In this article a scheme which preserves the dispersion relation for convective terms is proposed for solving the two-dimensional incompressible Navier-Stokes equations on nonstaggered grids. For the sake of computational efficiency, the splitting methods of Adams-Bashforth and Adams-Moulton are employed in the predictor and corrector steps, respectively, to render second-order temporal accuracy. For the sake of convective stability and dispersive accuracy, the linearized convective terms present in the predictor and corrector steps at different time steps are approximated by a dispersion relation-preserving (DRP) scheme. The DRP upwinding scheme developed within the 13-point stencil framework is rigorously studied by virtue of dispersion and Fourier stability analyses. To validate the proposed method, we investigate several problems that are amenable to exact solutions. Results with good rates of convergence are obtained for both scalar and Navier-Stokes problems.

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“…This is due to the fact that the energy of a convective system travels at the group velocity. This aspect of chosen numerical scheme in preserving dispersion relation is discussed in [26]. For the one-dimensional wave equation the physical group velocity is given by c. The numerical group velocity V gN can be found out from the numerical dispersion relation…”

Section: Analysis Of One-dimensional Wave Equationmentioning

confidence: 99%

“…In the next section we investigate these two time integration schemes for different explicit spatial schemes for the onedimensional wave equation. We will use the spectral analysis tool that is developed in [26] for analyzing any general discretization scheme. In Sec.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Time Advancement Methods for Solving Navier–Stokes Equations

Sengupta¹,

Dipankar

2004

Journal of Scientific Computing

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A qualitative and quantitative study is made for choosing time advancement strategies for solving time dependent equations accurately. A single step, low order Euler time integration method is compared with Adams-Bashforth, a second order accurate time integration strategy for the solution of one dimensional wave equation. With the help of the exact solution, it is shown that the presence of the computational mode in Adams-Bashforth scheme leads to erroneous results, if the solution contains high frequency components. This is tested for the solution of incompressible Navier-Stokes equation for uniform flow past a rapidly rotating circular cylinder. This flow suffers intermittent temporal instabilities implying presence of high frequencies. Such instabilities have been noted earlier in experiments and high accuracy computations for similar flow parameters. This test problem shows that second order AdamsBashforth time integration is not suitable for DNS.

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Analysis of central and upwind compact schemes

Cited by 169 publications

References 25 publications

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

Development of a Dispersion Relation-Preserving Upwinding Scheme for Incompressible Navier–Stokes Equations on NonStaggered Grids

A Comparative Study of Time Advancement Methods for Solving Navier–Stokes Equations

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