Choosing norms in adaptive FSI calculations

Birken, Philipp; Quint, Karsten J.; Hartmann, Stefan; Meister, Andreas

doi:10.1002/pamm.201010270

Cited by 10 publications

(11 citation statements)

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“…A fixed tolerance of 1e−8 is chosen for all involved equation solvers. The coupling code used has been developed in a series of papers [4,6,7]. It's main feature is time adaptivity, which is not employed here.…”

Section: Thermal Fsi Test Casesmentioning

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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Section: Thermal Fsi Test Casesmentioning

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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“…There, so called explicit first stage, singly diagonally implicit Runge-Kutta schemes (ESDIRK) are employed and higher order in time is proved by numerical results. The master program of the FSI procedure can be extended to SDIRK methods and furthermore, time adaptivity can be added into this framework as explained in [9,10]. Another interesting alternative is subcycling, where in the subsolvers, different time step sizes are chosen [21,37].…”

Section: Partitioned Coupling Methodsmentioning

confidence: 99%

“…Butcher array for SDIRK2. [10,9]. Basis is a master program that does the global time stepping and calls functions available in the subsolvers.…”

Section: Time Adaptive Methodsmentioning

confidence: 99%

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4. Numerical methods for unsteady thermal fluid structure interaction

Birken¹,

Monge

2017

Fluid-Structure Interaction

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We discuss thermal fluid structure interaction processes, where a simulation of the time dependent temperature field is of interest. Thereby, we consider partitioned coupling schemes with a Dirichlet-Neumann method. We present an analysis of the method on a model problem of discretized coupled linear heat equations. This shows that for large quotients in the heat conductivities, the convergence rate will be very small. The time dependency makes the use of time adaptive implicit methods imperative. This gives rise to the question, how accurate the appearing nonlinear systems should be solved, which is discussed in detail for both the nonlinear and linear case. The efficiency of the resulting method is demonstrated using realistic test cases.

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“…Several strategies exist to compute the relaxation parameter !. (12) and (13). An improvement in the scalar case is given by the secant method…”

Section: Aitken Relaxationmentioning

confidence: 99%

Fast solvers for unsteady thermal fluid structure interaction

Birken¹,

Gleim

Kuhl

et al. 2015

Numerical Methods in Fluids

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Summary We consider time‐dependent thermal fluid structure interaction. The respective models are the compressible Navier–Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet–Neumann method and a fixed point iteration is employed. As a reference solver, a previously developed efficient time‐adaptive higher‐order time integration scheme is used. To improve on this, we work on reducing the number of fixed point coupling iterations. Using the idea of extrapolation based on data given from the time integration by deriving such methods for SDIRK2, it is possible to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic. This leads to schemes that can use less than two iterations per time step. Furthermore, widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested, namely Aitken relaxation, minimal polynomial extrapolation and reduced rank extrapolation. These have no beneficial effects. Copyright © 2015 John Wiley & Sons, Ltd.

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Choosing norms in adaptive FSI calculations

Cited by 10 publications

References 1 publication

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

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

4. Numerical methods for unsteady thermal fluid structure interaction

Fast solvers for unsteady thermal fluid structure interaction

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