High order numerical simulation of aeolian tones

Müller, Bernhard

doi:10.1016/j.compfluid.2007.02.008

Cited by 39 publications

(38 citation statements)

References 25 publications

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“…Therefore, an explicit sixth‐order low‐pass filter is applied after each time step. The coefficient constant is chosen such that the waves with wave number k = π / h is annihilated . Studies by Visbal and Gaitonde provide strong evidence that those waves can be successfully suppressed by applying higher‐order spatial filters.…”

Section: Methodsmentioning

confidence: 99%

“…In this study, the 2D compressible Navier‐Stokes equations in perturbation form are solved. The perturbation formulation is employed to minimize cancelation errors when discretizing the Navier‐Stokes equations for compressible low Mach number flow . The conservative form of the 2D compressible Navier‐Stokes equations in perturbation formulation can be written as

{boldU}_{t}^{'} + {F^{c}}_{x}^{'} + {G^{c}}_{y}^{'} = {F^{v}}_{x}^{'} + {G^{v}}_{y}^{'} .

U ′ = U − U 0 is the vector of conservative perturbation variables with U =( ρ , ρ u , ρ v , ρ E ) T being the vector of the conservative variables and U 0 = ( ρ 0 ,0,0,( ρ E ) 0 ) T being the stagnation values.…”

Section: Compressible Navier‐stokes Equationsmentioning

confidence: 99%

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High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

Khalili

Larsson²,

Müller

2018

Numerical Methods in Fluids

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Summary A high‐order immersed boundary method is devised for the compressible Navier‐Stokes equations by employing high‐order summation‐by‐parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high‐order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross‐section of a human upper airway is simulated.

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Section: Methodsmentioning

confidence: 99%

{boldU}_{t}^{'} + {F^{c}}_{x}^{'} + {G^{c}}_{y}^{'} = {F^{v}}_{x}^{'} + {G^{v}}_{y}^{'} .

Section: Compressible Navier‐stokes Equationsmentioning

confidence: 99%

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

Khalili

Larsson²,

Müller

2018

Numerical Methods in Fluids

Self Cite

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show abstract

“…The field of high-order methods has seen a surge of research activity over the last decade, particularly due to its potential in applications such as LES [30][31][32][33][34], DNS [35][36][37], Computational Aero-Acoustics (CAA) [38,39], turbulent combustion [40] and vortex-dominated flows [41]. However, this field has not yet reached the level of maturity required to solve real flow problems on complicated geometries.…”

Section: Challenges and Strategies With Using High-order Methodsmentioning

confidence: 99%

High accuracy flow simulations: Advances and challenges for future needs in aeronautics

2011

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“…The perturbation formulation is employed to minimize cancellation errors when discretizing the Navier-Stokes equations for compressible low Mach number flow (Sesterhenn et al, 1999;Müller, 2008). The conservative form of the 2D compressible Navier-Stokes equations in perturbation formulation can be written as…”

Section: Fluid Flowmentioning

confidence: 99%

“…This fluid solver has been validated in previous investigations (Müller, 2008;Larsson and Müller, 2012) for single-domain structured grids.…”

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confidence: 99%

Interaction between a simplified soft palate and compressible viscous flow

Khalili

Larsson

Müller

2016

Journal of Fluids and Structures

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Fluid-structure interaction in a simplified 2D model of the upper airways is simulated to study flow-induced oscillation of the soft palate in the pharynx. The goal of our research has been a better understanding of the mechanisms of the Obstructive Sleep Apnea Syndrome and snoring by taking into account compressible viscous flow. The inspiratory airflow is described by the 2D compressible Navier-Stokes equations, and the soft palate is modeled as a flexible plate by the linearized EulerBernoulli thin beam theory. Fluid-structure interaction is handled by the arbitrary LagrangianEulerian formulation. The fluid flow is computed by utilizing 4 th order accurate summation by parts difference operators and the 4 th order accurate classical Runge-Kutta method which lead to very accurate simulation results. The motion of the cantilevered plate is solved numerically by employing the Newmark time integration method. The numerical schemes for the structure are verified by comparing the computed frequencies of plate oscillation with the associated second mode eigenfrequency in vacuum. Vortex dynamics is assessed for the coupled fluid-structure system when both airways are open and when one airway is closed. The effect of mass ratio, rigidity and damping coefficient of the plate on the oscillatory behaviour is investigated. An acoustic analysis is carried out to characterize the acoustic wave propagation induced by the plate oscillation. It is observed that the acoustic wave corresponding to the quarter wave mode along the length of the duct is the dominant frequency. However, the frequency of the plate oscillation is recognizable in the acoustic pressure when reducing the amplitude of the quarter wave mode.

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High order numerical simulation of aeolian tones

Cited by 39 publications

References 25 publications

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

High accuracy flow simulations: Advances and challenges for future needs in aeronautics

Interaction between a simplified soft palate and compressible viscous flow

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