Stability Analysis of Interface Temporal Discretization in Grid Overlapping Methods

Peet, Yulia; Fischer, Paul

doi:10.1137/110831234

Cited by 18 publications

(20 citation statements)

References 38 publications

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“…Search and locate procedures are carried out to express the location of a point on the interface of one subdomain in terms of the local coordinates of a corresponding element in the other subdomain. Temporal coupling at interfaces is achieved using up to a third-order explicit interface extrapolation scheme (IEXT3), using interpolated values from previous time steps [44,56].…”

Section: Methodsmentioning

confidence: 99%

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Merrill

Peet

2017

AIAA Journal

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Dynamically moving airfoils are encountered in helicopter rotors, wind-turbine blades, and maneuvering aircraft. A clearer understanding of how freestream disturbances affect the aerodynamic forces on pitching airfoils leads to improved designs. In the present study, the authors' recently validated spectrally accurate moving overlapping mesh methodology is used to perform a direct numerical simulation of a NACA 0012 airfoil pitching with oscillatory motion in the presence of a turbulent wake created by an upstream solid cylinder. The global computational domain is decomposed into a stationary background mesh, which contains the solid cylinder, and a mesh constructed around the airfoil that is constrained to pitch with predetermined reduced frequency k 0.16. Present simulations are performed with chord-based Reynolds number Re c 44;000. Aerodynamic forces and vortex-shedding properties are compared between the pitching airfoil simulations with and without upstream disturbances. Power spectral density functions of the aerodynamic forces and moments are investigated to further determine the effect of a turbulent wake on a pitching airfoil.

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Section: Methodsmentioning

confidence: 99%

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Merrill

Peet

2017

AIAA Journal

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“…(The nonlinear term is already accurately treated by extrapolation and is stable provided one adheres to standard CFL stability limits.) Typically three to five subiterations (κ iter ) are needed per timestep to ensure stability [24] for mthorder extrapolation of the interface boundary data, when m > 1. Using this approach, Merrill et al [21] demonstrated exponential convergence in space and up to third-order accuracy in time for Schwarz-SEM flow applications.…”

Section: Sem-schwarz For Navier-stokesmentioning

confidence: 99%

Nonconforming Schwarz-spectral element methods for incompressible flow

2019

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We present scalable implementations of spectral-element-based Schwarz overlapping (overset) methods for the incompressible Navier-Stokes (NS) equations. Our SEM-based overset grid method is implemented at the level of the NS equations, which are advanced independently within separate subdomains using interdomain velocity and pressure boundarydata exchanges at each timestep or sub-timestep. Central to this implementation is a general, robust, and scalable interpolation routine, gslib-findpts, that rapidly determines the computational coordinates (processor p, element number e, and local coordinates (r, s, t) ∈Ω := [−1, 1] 3 ) for any arbitrary point x * = (x * , y * , z * ) ∈ Ω ⊂ lR 3 . The communication kernels in gslib execute with at most log P complexity for P MPI ranks, have scaled to P > 10 6 , and obviate the need for development of any additional MPI-based code for the Schwarz implementation. The original interpolation routine has been extended to account for multiple overlapping domains. The new implementation discriminates the possessing subdomain by distance to the domain boundary, such that the interface boundary data is taken from the inner-most interior points. We present application of this approach to several heat transfer and fluid dynamic problems, discuss the computation/communication complexity and accuracy of the approach, and present performance measurements for P > 12, 000.

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“…However, the convergence rate is not great for some FSI couplings, which is why a lot of effort goes into convergence acceleration [10]. An alternative are optimized Schwarz methods [13,15,29] and the CHAMP scheme (Conjugate Heat transfer Advanced Multidomain Partitioned) which uses a generalized Robin (mixed) condition at the interface to accelerate the iteration [24], but overlapping domains. Furthermore, for incompressible fluids it is known that the ratio of densities of the materials plays an important role [1,9].…”

Section: Introductionmentioning

confidence: 99%

On the convergence rate of the Dirichlet–Neumann iteration for unsteady thermal fluid–structure interaction

Monge

Birken

2017

Comput Mech

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We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations with jumps in the material coefficients across the interface. The heat equations are discretized using an implicit Euler scheme in time, whereas a finite element method on one domain and a finite volume method with variable aspect ratio on the other one are used in space. We provide an exact formula for the spectral radius of the iteration matrix. The formula indicates that for large time steps, the convergence rate is the aspect ratio times the quotient of heat conductivities and that decreasing the time step will improve the convergence rate. Numerical results confirm the analysis and show that the 1D formula is a very good estimator in 2D and even for nonlinear thermal FSI applications.

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Stability Analysis of Interface Temporal Discretization in Grid Overlapping Methods

Cited by 18 publications

References 38 publications

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Nonconforming Schwarz-spectral element methods for incompressible flow

On the convergence rate of the Dirichlet–Neumann iteration for unsteady thermal fluid–structure interaction

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