Manfred Kaltenbacher in cooperation with A. Hppe, I. Sim - - PowerPoint PPT Presentation
Spectral finite elements for a mixed formulation in computational acoustics taking flow effects into account Manfred Kaltenbacher in cooperation with A. Hppe, I. Sim (University of Klagenfurt), G. Cohen and S. Imperial (INRIA, Paris) and B.
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
(INRIA, Paris) and B. Wohlmuth (TU Munich)
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Pierce equation Acoustic perturbation equation
Acoustic conservation equations
Comparison to wave equation with pFEM
Acoustic perturbation equations Occurring instabilities Stabilization (flux term and dissipative term) Application to aeroacoustics
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Mean quantities Alternating quantities (disturbances)
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Subset of linearized Euler equations Support just
Fully considers
Journal of Computational Physics, 2003
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Equation Acoustic Conservation Equations
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Discrete spaces1
Journal of Computational Acoustics, 2000
Piola transform Lagrange polynomial space of order N Mapping:
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Preserves the normal component! Term with gradient Term with divergence
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Elements Semidiscrete Galerkin formulation
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Excitation with a sine pulse of main wavelength λ Reference solution obtained with h= λ/120 and Δt= 1/(f 200) Computational mesh with mean element size of λ/5 and Δt<=λ /(2*c) Time Stepping:
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Pressure Field
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Conservation equations
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Piola transform
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Initial condition Flow
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Piola transform
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Central flux term Reverse integration by parts on
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Averaging leads to Add penalty (dissipative) term
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Spurious waves
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
URANS CFD computations (Fluent, Michele Degenaro, AIT, Vienna) Mach number about 0.3
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Lighthill analogy Acoustic Perturbation equation (APE) RHS of Lighthill’s equation Test function RHS of APE Lamb vector
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Without flow With flow
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Acoustic perturbation equation Pierce equation PML layer Non-matching grid interface (Mortar framework)
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Continuity of pressure Continuity of normal component of particle velocity Lagrange multiplier
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011
Acoustic perturbation equation Pierce equation Continuity of pressure in a weak sense
Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM, 2011