GMRES applied to the Time Spectral and Quasi-periodic Time Spectral Methods

Mundis, Nathan L.; Mavriplis, Dimitri J.

doi:10.2514/6.2013-3084

Cited by 12 publications

(11 citation statements)

References 8 publications

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“…To demonstrate the accuracy of a moving grid in an overset framework a simulation of a pitching NACA 0012 airfoil is carried out [49]. The airfoil pitches at the quarter chord with a time dependent angle given by the formula:…”

Section: Pitching Airfoilmentioning

confidence: 99%

An overset mesh approach for 3D mixed element high-order discretizations

Brazell

Sitaraman

Mavriplis

2016

Journal of Computational Physics

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A parallel high-order Discontinuous Galerkin (DG) method is used to solve the compressible Navier-Stokes equations in an overset mesh framework. The DG solver has many capabilities including: hp-adaption, curved cells, support for hybrid, mixed-element meshes, and moving meshes. Combining these capabilities with overset grids allows the DG solver to be used in problems with bodies in relative motion and in a near-body offbody solver strategy. The overset implementation is constructed to preserve the design accuracy of the baseline DG discretization. Multiple simulations are carried out to validate the accuracy and performance of the overset DG solver. These simulations demonstrate the capability of the high-order DG solver to handle complex geometry and large scale parallel simulations in an overset framework.

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Section: Pitching Airfoilmentioning

confidence: 99%

An overset mesh approach for 3D mixed element high-order discretizations

Brazell

Sitaraman

Mavriplis

2016

Journal of Computational Physics

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“…Evaluation of the temporal derivative source term is achieved by a sequence of 2b Message-Passing Interface (MPI) calls, where b is the bandwidth of the operator. For the case of the Time-Spectral method, b = N/2 or (N − 1) /2 and the process executes in a ring topology [61] where each process multiples its solution by the appropriate element of the D N matrix and passes it to the subsequent process (time sample) to be aggregated using MPI_sendrecv_replace. For the case of the FDMT-p approach, only p MPI_sendrecv calls are required to the M = p/2 neighboring processes.…”

Section: Vc Parallel-in-time Modulementioning

confidence: 99%

Towards Efficient Parallel-in-Time Simulation of Periodic Flows

Leffell

Sitaraman

Lakshminarayan

et al. 2016

54th AIAA Aerospace Sciences Meeting

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In response to the stagnation of computer microprocessor speeds over the past decade, the design emphasis of novel supercomputing architectures has focused primarily on increasing the overall number of available cores and reducing communication bottlenecks. Typically, flow solvers have been able to achieve parallel efficiency using domain decomposition, but this approach has the natural limitation that saturation will manifest itself on a finite number of cores at which point parallel speedup stalls and eventually deteriorates. In order to improve parallel scalability we seek to leverage the existing knowledge base on spatial decomposition, while attempting to exploit additional parallelism in the temporal dimension. Specifically, we explore the case of time periodic flows using Parallel-in-Time (PinT) variants of the Time-Spectral (TS) method. A framework employing a Pythonbased infrastructure is described including a standalone library that can be coupled to existing flow solvers in order to facilitate PinT calculations. A model problem of a periodic density pulse is used to examine the different discretization options. Implications for application to wind turbines and rotors are addressed.

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“…In the context of implicit time‐spectral methods for CFD, in Refs. and , GMRES methods were preconditioned using a block‐colored Gauss‐Seidel solver and multigrid, respectively.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…In the context of implicit timespectral methods for CFD, in Refs. [22] and [10], GMRES methods were preconditioned using a block-colored Gauss-Seidel solver and multigrid, respectively. In the current work, we choose right preconditioning with a preconditioner that consists of an approximate factorization of an approximation to the complete Jacobian given in Equation (11).…”

Section: Preconditioningmentioning

confidence: 99%

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Jacobian‐free Newton–Krylov method for implicit time‐spectral solution of the compressible Navier‐Stokes equations

Attar

2015

Numerical Methods in Fluids

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Summary We introduce a Jacobian‐free Newton–Krylov method for the implicit time‐spectral solution of the compressible Navier‐Stokes equations. A new type of preconditioner is presented, which is based upon an approximate factorization of an approximation to the exact time‐spectral Jacobian. The choice of this type of preconditioner is particularly useful when the time‐spectral scheme is to be implemented into a computational code that already contains an implicit time‐marching solver. The spatial discretization of the Navier–Stokes equation consists of a sixth‐order compact scheme with a high‐order, low‐pass filter. Numerical simulation of the laminar flow over a circular cylinder at two post‐critical Reynolds numbers (Re=50,100) is used to characterize the performance of the method. In general, the time‐spectral solution is two to ten times faster, for equivalent accuracy in the lift coefficient, than a time‐marching implicit Beam‐Warming solution with the upper end of this range noted when the Reynolds number is closer to the dynamic instability bifurcation Reynolds number. Other numerical and analytical results are presented, which demonstrate various aspects of the preconditioner performance. In addition, results and discussion are given for some characteristics of time‐spectral solutions for autonomous problems where the fundamental frequency is unknown. Copyright © 2015 John Wiley & Sons, Ltd.

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GMRES applied to the Time Spectral and Quasi-periodic Time Spectral Methods

Cited by 12 publications

References 8 publications

An overset mesh approach for 3D mixed element high-order discretizations

An overset mesh approach for 3D mixed element high-order discretizations

Towards Efficient Parallel-in-Time Simulation of Periodic Flows

Jacobian‐free Newton–Krylov method for implicit time‐spectral solution of the compressible Navier‐Stokes equations

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