Block-Jacobi Implicit Algorithms for the Time Spectral Method

Sicot, Frédéric; Puigt, Guillaume; Montagnac, Marc

doi:10.2514/1.36792

Cited by 80 publications

(43 citation statements)

References 16 publications

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“…The published information is scarce (see [4], for instance, for the LUR) regarding detailed and consistent CPU time requirement comparisons of the two methods with URANS (for example, Hall et al [5] compare their approach to steady computations). As can be expected, it appears to be problem and implementation dependant (compare [9,10], for instance). A second objective of the present paper is thus to make the assessment over a range of significantly different flow conditions, but for the same physical problem and within the same code.…”

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confidence: 89%

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Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Dufour¹,

Sicot²,

Puigt³

et al. 2010

AIAA Journal

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In the framework of unsteady aerodynamics, forced-harmonic-motion simulations can be used to compute unsteady loads. In this context, the present paper assesses two alternatives to the unsteady Reynolds-averaged Navier-Stokes approach, the linearized unsteady Reynolds-averaged Navier-Stokes equations method, and the harmonic balance approach. The test case is a NACA 64A006 airfoil with an oscillating flap mounted at 75% of the chord. Emphasis is put on examining the performances of the methods in terms of accuracy and computational cost over a range of physical conditions. It is found that, for a subsonic flow, the linearized unsteady Reynolds-averaged Navier-Stokes method is the most efficient one. In the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method remains the fastest approach, but with limited accuracy around shocks, whereas a oneharmonic harmonic balance solution is in closer agreement with the unsteady Reynolds-averaged Navier-Stokes solution. In the case of separation in the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method fails to converge, whereas the harmonic balance remains robust and accurate.

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confidence: 89%

“…In the present paper the notation HB is retained, though all the computations presented here consider a single fundamental frequency. This method has proven its efficiency in decreasing the total CPU time of forced-motion simulations, while ensuring a good accuracy (see Sicot et al [9], among others).…”

mentioning

confidence: 99%

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Dufour¹,

Sicot²,

Puigt³

et al. 2010

AIAA Journal

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“…This restriction can be removed by resorting to an implicit approach in pseudo-time. Such an approach has been derived in reference [16] using a first-order backwards difference scheme in pseudo time.…”

Section: Fully Implicit Methodsmentioning

confidence: 99%

“…However, it is well known that this approach suffers stability restrictions and results in convergence degradation as the number of harmonics increases [6]. In this work, we employ a fully (time and space) implicit solution strategy originally described by Sicot [16] which in principle is capable of delivering convergence rates that are independent of the number of harmonics or time instances used in the time-spectral discretization. This approach is further accelerated through the application of a line-implicit agglomeration multigrid algorithm applied to the spatially implicit system.…”

Section: Introductionmentioning

confidence: 99%

Time Spectral Method for Periodic and Quasi-Periodic Unsteady Computations on Unstructured Meshes

Mavriplis

Yang

2011

Math. Model. Nat. Phenom.

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Abstract. For flows with strong periodic content, time-spectral methods can be used to obtain time-accurate solutions at substantially reduced cost compared to traditional time-implicit methods which operate directly in the time domain. However, these methods are only applicable in the presence of fully periodic flows, which represents a severe restriction for many aerospace engineering problems. This paper presents an extension of the time-spectral approach for problems that include a slow transient in addition to strong periodic behavior, suitable for applications such as transient turbofan simulation or maneuvering rotorcraft calculations. The formulation is based on a collocation method which makes use of a combination of spectral and polynomial basis functions and results in the requirement of solving coupled time instances within a period, similar to the time spectral approach, although multiple successive periods must be solved to capture the transient behavior.The implementation allows for two levels of parallelism, one in the spatial dimension, and another in the time-spectral dimension, and is implemented in a modular fashion which minimizes the modifications required to an existing steady-state solver. For dynamically deforming mesh cases, a formulation which preserves discrete conservation as determined by the Geometric Conservation Law is derived and implemented. A fully implicit approach which takes into account the coupling between the various time instances is implemented and shown to preserve the baseline steady-state multigrid convergence rate as the number of time instances is increased. Accuracy and efficiency are demonstrated for periodic and non-periodic problems by comparing the performance of the method with a traditional time-stepping approach using a simple two-dimensional pitching airfoil problem, a three-dimensional pitching wing problem, and a more realistic transitioning rotor problem.

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“…Mosahebi extended the method for nonlinear problems and developed an adapted approach for two-dimensional viscous flows using the NLFD approach [57], and demonstrated its application on deformable grids [59]. Originally developed using explicit solvers such as Runge-Kutta methods for the advancement of pseudotime, the convergence speed of frequency-domain methods was improved by the use of implicit algorithms such as block-Jacobi for the TS method [75] and Lower-Upper Symmetric Gauss-Seidel (LU-SGS) for the adaptive NLFD method [58].…”

Section: Frequency-domain Solution Methodsmentioning

confidence: 99%

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

Tardif

Nadarajah

2017

AIAA Journal

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Block-Jacobi Implicit Algorithms for the Time Spectral Method

Cited by 80 publications

References 16 publications

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Time Spectral Method for Periodic and Quasi-Periodic Unsteady Computations on Unstructured Meshes

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

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