Direct Numerical Simulation of Spatial Transition to Turbulence Using Fourth-Order Vertical Velocity Second-Order Vertical Vorticity Formulation

Bhaganagar, Kiran; Rempfer, Dietmar; Lumley, John L.

doi:10.1006/jcph.2002.7088

Cited by 24 publications

(30 citation statements)

References 28 publications

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“…The time step ∆t = t n+1 − t n is constant in the interval of interest. In addition to (3), w n+1 satisfies the discretization of the divergence equation in (2). The result is a linear system of equations to solve for w n+1 and p n+1 in every time step.…”

Section: Time Discretizationmentioning

confidence: 99%

“…A common combination is the Adams-Bashforth method of second order and the implicit trapezoidal (or Crank-Nicolson) method [24], [28], [37]. The Crank-Nicolson scheme is combined with an explicit Runge-Kutta method in [2].…”

Section: N+1mentioning

confidence: 99%

“…An overview of iterative methods and preconditioners for (17) is found in [10] and the convergence of a particular preconditioning operator is analyzed in [12] and applied in [11]. The multigrid method is applied to the solution of the incompressible Navier-Stokes equations in [2], [15], [31], [36]. A possibility is to apply the multigrid algorithm only to (25) instead of the ILU preconditioner.…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

“…The nonlinear convection term N is extrapolated from the previous time steps. The linear part of the discretized momentum equations L and the discretized divergence equation (2) are solved simultaneously at the new time level. A system of linear equations has to be solved for w and p in every time step.…”

Section: Introductionmentioning

confidence: 99%

“…Other finite difference methods of high order for the Navier-Stokes equations are found in [2], [22], [27], [29], [32], [33], [40]. The velocity-vorticity equations are solved in [2] with a fourth order compact method and advanced in time by a semi-implicit scheme. The stencil is a wide fourth order centered difference in [22] applied to the equations (1) and in [29] the fourth order differential equation for the streamfunction is discretized by fourth order centered differences.…”

Section: Introductionmentioning

confidence: 99%

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High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.

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Section: Time Discretizationmentioning

confidence: 99%

Section: N+1mentioning

confidence: 99%

Section: Comparison With Other Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational Fluid Dynamics

2016

Computational Electromagneticaerodynamics

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In this paper, Computational fluid Dynamics (CFD) is used to predict accurately the incremental lift due to use of passive lift -augmentation device 'Flap'. In a 2-D wing, lift at a given angle of attack can be increased by increasing camber. In aircraft design, values of Maximum Lift Coefficient (C L max ) are used to determine the take-off and landing distances, on the assumption of usage of some type of lift-enhancing device. Passive lift enhancement device, such as a trailing edge plain flap, is relevant to most of the aircraft designs except Short Take Off and Landing (STOL) However, accurate analytical solutions to complex non linear equations of aerodynamics are a far cry and one has to depend largely on support from experimental results. It is here that CFD analysis makes the task simpler. Computational study of a typical plain flap with NACA (National Advisory Committee for Aeronautics) 0012 airfoil is taken up to predict its influence on incrementing the lift during critical phases of flight at low speed. The flow analysis is done using CFD tool FLUENT 6.3 along with GAMBIT 2.2. Effect of Plain flaps on basic aerodynamic parameters such as C P , C L , C D are studied by analyzing the flow over an airfoil with plain flap. The results obtained from the analysis are compared with analytical solutions to establish the influence and relevance of flap as an effective high lift device.

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A high‐order accurate method for two‐dimensional incompressible viscous flows

Eswaran

2006

Numerical Methods in Fluids

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SUMMARYA high-order accurate solution method for complex geometries is developed for two-dimensional flows using the stream function-vorticity formulation. High-order accurate spectrally optimized compact schemes along with appropriate boundary schemes are used for spatial discretization while a two-level backward Euler implicit scheme is used for the time integration. The linear system of equations for stream function and vorticity are solved by an inner iteration while contravariant velocities constitute outer iterations. The effect of curvilinear grids on the solution accuracy is studied. The method is used to compute Cartesian and inclined driven cavity, flow in a triangular cavity and viscous flow in constricted channel. Benchmark-like accuracy is obtained in all the problems with fewer grid points compared to reported studies.

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Direct Numerical Simulation of Spatial Transition to Turbulence Using Fourth-Order Vertical Velocity Second-Order Vertical Vorticity Formulation

Cited by 24 publications

References 28 publications

High order accurate solution of the incompressible Navier–Stokes equations

High order accurate solution of the incompressible Navier–Stokes equations

Computational Fluid Dynamics

A high‐order accurate method for two‐dimensional incompressible viscous flows

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