An Unfactored Implicit Moving Mesh Method for the Two-Dimensional Unsteady N-S Equations

Badcock, K. J.; Gaitonde, Ann L

doi:10.1002/(sici)1097-0363(19960930)23:6<607::aid-fld433>3.0.co;2-e

Cited by 18 publications

(12 citation statements)

References 20 publications

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“…Comparison between the computed and experimental data is considered satisfactory. The present correlation compares favourably with those obtained by other authors [27,28].…”

Section: Pitching Oscillationssupporting

confidence: 92%

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Study of the aerodynamics of in-plane motion

Shaw

Qin

2001

Proceedings of the Institution of Mechanical Engineers, Part G:

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A computational analysis is performed of the unsteady aerodynamics associated with the blade sections of helicopter rotors in forward flight. The unsteady flow is studied through solutions of the twodimensional Reynolds averaged Navier-Stokes equations together with a strongly coupled two-equation model of turbulence. Two motions are studied.The first motion is that of an aerofoil subjected to harmonic in-plane oscillations. The influence of advance ratio and reduced frequency is investigated. It is shown that, in the absence of shock waves, the flow is periodic with a reduced frequency equal to that of the forcing motion. However, the flow development lags behind the forcing motion. Furthermore, for constant reduced frequency the phase lag is independent of advance ratio.In addition to harmonic motion, the aerodynamic response to a step change in Mach number is investigated. Using an assumed form of the response of lift coefficient to a step change in Mach number, a lift transfer operator for step changes in Mach number is obtained in the Laplace domain. An analytical expression for the response to harmonic Mach number oscillations is then obtained from the transfer operator. The resulting formulation for the aerodynamic response confirms that the lag between the forcing motion and the aerodynamic response is independent of advance ratio.

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“…Comparison between the computed and experimental data is considered satisfactory. The present correlation compares favourably with those obtained by other authors [27,28].…”

Section: Pitching Oscillationssupporting

confidence: 92%

“…where the phase angle ö n is obtained from the ratio of the constants ð 1, n and ð 2, n using tan(ö n )ˆð 1,n öð 2,nˆ1 öT n (28) …”

Section: Appendixmentioning

confidence: 99%

Study of the aerodynamics of in-plane motion

Shaw

Qin

2001

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…Note that using this approach, a non-iterative implicit method, see e.g. Reference [21], obtained by linearizing R(Q n + 1 ) in (3) does not fully employ the turbulence model in a strict sense for unsteady flows, since some terms are omitted in the left-hand side. However, in the Newton-like method employed here, despite the absence of these terms the turbulence model is fully accounted for in the final solution through the sub-iterations.…”

Section: Con6ergence For the Unsteady Casesmentioning

confidence: 99%

“…Badcock et al [20,21] have recently developed an efficient preconditioning procedure based on an approximate factorization (AF) for an unfactored implicit scheme. Although the method is not a Newton-like method, an analytical Jacobian was obtained with the help of a symbolic package (REDUCE) and is stored and used in the linearized unfactored implicit solution.…”

Section: Introductionmentioning

confidence: 99%

A matrix-free preconditioned Newton/GMRES method for unsteady Navier-Stokes solutions

Qin

Ludlow

Shaw

2000

Int. J. Numer. Meth. Fluids

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The unsteady compressible Reynolds‐averaged Navier–Stokes equations are discretized using the Osher approximate Riemann solver with fully implicit time stepping. The resulting non‐linear system at each time step is solved iteratively using a Newton/GMRES method. In the solution process, the Jacobian matrix–vector products are replaced by directional derivatives so that the evaluation and storage of the Jacobian matrix is removed from the procedure. An effective matrix‐free preconditioner is proposed to fully avoid matrix storage. Convergence rates, computational costs and computer memory requirements of the present method are compared with those of a matrix Newton/GMRES method, a four stage Runge–Kutta explicit method, and an approximate factorization sub‐iteration method. Effects of convergence tolerances for the GMRES linear solver on the convergence and the efficiency of the Newton iteration for the non‐linear system at each time step are analysed for both matrix‐free and matrix methods. Differences in the performance of the matrix‐free method for laminar and turbulent flows are highlighted and analysed. Unsteady turbulent Navier–Stokes solutions of pitching and combined translation–pitching aerofoil oscillations are presented for unsteady shock‐induced separation problems associated with the rotor blade flows of forward flying helicopters. Copyright © 2000 John Wiley & Sons, Ltd.

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“…Normal force and pitching moment coefficients are shown in Figure 9(a and b), respectively, in which the overall agreement between the two codes can be determined. To explain the relatively large difference for the pitching moment coefficient between the RANS results and the experimental data, published results in [31] showed that the pitching moment value is sensitive to the moment centre used. Figure 10 presents unsteady pressure distributions at two instantaneous angles of attack during the cycle for turbulent flow.…”

Section: Unsteady Turbulent Flow-agard Ct1mentioning

confidence: 99%

An implicit meshless method for application in computational fluid dynamics

Kennett

Timme

Angulo

et al. 2012

Numerical Methods in Fluids

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SUMMARY An implicit meshless scheme is developed for solving the Euler equations, as well as the laminar and Reynolds‐averaged Navier–Stokes equations. Spatial derivatives are approximated using a least squares method on clouds of points. The system of equations is linearised, and solved implicitly using approximate, analytical Jacobian matrices and a preconditioned Krylov subspace iterative method. The details of the spatial discretisation, linear solver and construction of the Jacobian matrix are discussed; and results that demonstrate the performance of the scheme are presented for steady and unsteady two dimensional fluid flows. Copyright © 2012 John Wiley & Sons, Ltd.

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An Unfactored Implicit Moving Mesh Method for the Two-Dimensional Unsteady N-S Equations

Cited by 18 publications

References 20 publications

Study of the aerodynamics of in-plane motion

Study of the aerodynamics of in-plane motion

A matrix-free preconditioned Newton/GMRES method for unsteady Navier-Stokes solutions

An implicit meshless method for application in computational fluid dynamics

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