6 research outputs found
Convolution quadrature for the wave equation with impedance boundary conditions
We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem.
For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients.
Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation
Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions
This paper proves the asymptotic stability of the multidimensional wave
equation posed on a bounded open Lipschitz set, coupled with various classes of
positive-real impedance boundary conditions, chosen for their physical
relevance: time-delayed, standard diffusive (which includes the
Riemann-Liouville fractional integral) and extended diffusive (which includes
the Caputo fractional derivative). The method of proof consists in formulating
an abstract Cauchy problem on an extended state space using a dissipative
realization of the impedance operator, be it finite or infinite-dimensional.
The asymptotic stability of the corresponding strongly continuous semigroup is
then obtained by verifying the sufficient spectral conditions derived by Arendt
and Batty (Trans. Amer. Math. Soc., 306 (1988)) as well as Lyubich and V\~u
(Studia Math., 88 (1988))
Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations
Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impeda-nce, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow duct
Convolution quadrature for the wave equation with impedance boundary conditions
We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem.
For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients.
Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation