Influence of Weak and Strong Solid Wall Boundary Conditions on the Convergence to Steady-State of the Navier-Stokes Equations

Eliasson, Peter; Eriksson, Sofia; Nordström, Jan

doi:10.2514/6.2009-3551

Cited by 33 publications

(26 citation statements)

References 16 publications

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“…We continue the work in [10] and to some extent follow the procedure outlined in [12,29] for the analysis of far field boundary conditions. Our basic theoretical tools will be the classical ones, namely the energy method, the Laplace transform technique and the matrix exponential.…”

Section: Introductionmentioning

confidence: 99%

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

Nordström

Eriksson

Eliasson

2012

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

Nordström

Eriksson

Eliasson

2012

Journal of Computational Physics

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“…We have which proves Equation (35) due to the definition of α 4 . As the slow component is only coupled to the first micro step of the fast component, we have proving Equation (36).…”

Section: Corollary 3 (Third Order Coupling) If In Case (C) the Couplmentioning

confidence: 90%

“…Hence, the validity of Equations (35) and (36) remains to be shown. We have which proves Equation (35) due to the definition of α 4 .…”

Section: Corollary 3 (Third Order Coupling) If In Case (C) the Couplmentioning

confidence: 99%

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On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law

Bremicker-Trübelhorn

Ortleb

2017

Aerospace

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Abstract:The application of partitioned schemes to fluid-structure interaction (FSI) allows the use of already developed solvers specifically designed for the efficient solution of the corresponding subproblems. In this work, we propose and describe a loosely coupled partitioned scheme based on the recently introduced generalized-structure additively partitioned Runge-Kutta (GARK) framework. The resulting scheme combines implicit-explicit (IMEX) and multirate approaches while coupling of the subproblems is realized both on the level of the discrete time steps and at the level of interior Runge-Kutta stages. Specifically, we allow for varying micro step sizes for the fluid subproblem and therefore extend the multirate GARK framework based on constant micro steps. Furthermore, we derive the order conditions for this extension allowing for coupled time integration schemes of up to third order and discuss specific choices of the Runge-Kutta coefficients complying with the geometric conservation law. Finally, numerical experiments are carried out for uniform flow on a moving grid as well as the classical FSI test case of a moving piston.

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“…However in that paper a wide operator was used which have a different set of eigenvalues. It is beneficial for the rate of convergence to steady-state with a discretization which have its real parts of the spectrum bounded away from zero as far as possible [5,14,15,16]. In Figure 6 we show the real part of the spectrum closest to zero as a function of r. We have used 33 grid points for the single domain in both Figure 5 and Figure 6 and hence the coupled domains have 34 grid points in total.…”

Section: Stiffness and Convergence To Steady-statementioning

confidence: 99%

Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

Berg

Nordström

2012

Applied Numerical Mathematics

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In this paper we study the heat and advection equation in single and multiple domains. We discretize using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices. We show how the spectrum of the single domain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. We study the impact on the spectrum and discretization errors depending on the interface treatment and verify that the results are carried over to higher order accurate schemes.

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Influence of Weak and Strong Solid Wall Boundary Conditions on the Convergence to Steady-State of the Navier-Stokes Equations

Cited by 33 publications

References 16 publications

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law

Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

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