RADIATION AND OUTFLOW BOUNDARY CONDITIONS FOR DIRECT COMPUTATION OF ACOUSTIC AND FLOW DISTURBANCES IN A NONUNIFORM MEAN FLOW

1996 ◽  
Vol 04 (02) ◽  
pp. 175-201 ◽  
Author(s):  
CHRISTOPHER K.W. TAM ◽  
ZHONG DONG
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Maximum Velocity ◽  
Mean Flow ◽  
Direct Computation ◽  
Radiation Boundary Conditions ◽  
Outflow Boundary Conditions ◽  
The Mean ◽  
Radiation Boundary ◽  
Outflow Boundary

It is well known that Euler equations support small amplitude acoustic, vorticity and entropy waves. To perform high quality direct numerical simulations of flow generated noise problems, acoustic radiation boundary conditions are required along inflow boundaries. Along boundaries where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy disturbances to exit the computation domain without significant reflection. A set of radiation and outflow boundary conditions for problems with nonuniform mean flows are developed in this work. Flow generated acoustic disturbances are usually many orders of magnitude smaller than that of the mean flow. To capture weak acoustic waves by direct computation (without first separating out the mean flow), the intensity of numerical noise generated by the numerical algorithm and the radiation and outflow boundary conditions (and the computer) must be extremely low. It is demonstrated by a test problem involving sound generation by an oscillatory source that weak acoustic waves with maximum velocity fluctuation of the order of 10−9 of the mean flow velocity can be computed accurately using the proposed radiation boundary conditions. The intensity of such acoustic waves is much smaller than the numerical error of the mean flow solution.

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

scholarly journals Outgoing solutions and radiation boundary conditions for the ideal atmospheric scalar wave equation in helioseismology

2020 ◽  
Vol 54 (4) ◽  
pp. 1111-1138 ◽  
Author(s):  
Hélène Barucq ◽  
Florian Faucher ◽  
Ha Pham
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Whittaker Functions ◽  
Radiation Boundary Conditions ◽  
Time Harmonic ◽  
Whole Space ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map ◽  
Radiation Conditions ◽  
The Ideal

In this paper, we study the time-harmonic scalar equation describing the propagation of acoustic waves in the Sun’s atmosphere under ideal atmospheric assumptions. We use the Liouville change of unknown to conjugate the original problem to a Schrödinger equation with a Coulomb-type potential. This transformation makes appear a new wavenumber, k, and the link with the Whittaker’s equation. We consider two different problems: in the first one, with the ideal atmospheric assumptions extended to the whole space, we construct explicitly the Schwartz kernel of the resolvent, starting from a solution given by Hostler and Pratt in punctured domains, and use this to construct outgoing solutions and radiation conditions. In the second problem, we construct exact Dirichlet-to-Neumann map using Whittaker functions, and new radiation boundary conditions (RBC), using gauge functions in terms of k. The new approach gives rise to simpler RBC for the same precision compared to existing ones. The robustness of our new RBC is corroborated by numerical experiments.

HIGH-ORDER RADIATION BOUNDARY CONDITIONS FOR STRATIFIED MEDIA AND CURVILINEAR COORDINATES

2012 ◽  
Vol 20 (02) ◽  
pp. 1240002 ◽  
Author(s):  
THOMAS HAGSTROM
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Curvilinear Coordinates ◽  
Stratified Media ◽  
Computational Domain ◽  
Progressive Wave ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Radiation Boundary ◽  
Homogeneous Media

Optimized local radiation boundary conditions to truncate the computational domain by a rectangular boundary have been constructed for acoustic waves propagating into a homogeneous, isotropic far field. Here we try to achieve comparable efficiencies in stratified media and cylindrical coordinates. We find that conditions constructed for homogeneous media are highly effective in the stratified case. On the circle we derive boundary conditions by optimizing a semidiscretized perfectly matched layer. Though we are unsuccessful in matching the accuracies of the Cartesian case, our experiments show that older sequences based on the progressive wave expansion are surprisingly efficient.

On Boundary Conditions for Acoustic Computations in Non-Uniform Mean Flows

1997 ◽  
Vol 05 (03) ◽  
pp. 297-315 ◽  
Author(s):  
Thomas Z. Dong
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Near Field ◽  
Wave Radiation ◽  
Computational Domain ◽  
Mean Flow ◽  
Exterior Field ◽  
Artificial Boundary ◽  
Artificial Boundaries ◽  
The Mean

Many acoustic problems involve acoustic wave radiation to the exterior field. A common approach in numerical simulations is to restrict the computational domain to a finite region with artificial boundaries. The so-called radiation or non-reflecting boundary conditions must be imposed at those artificial boundaries. Most existing non-reflecting boundary conditions are derived for computing disturbances propagating in a known uniform mean flow near the boundaries. In many applications such as the computation of jet noise or turbofan noise, the mean flow at an artificial boundary is non-uniform and unknown. The mean flow also needs to be computed in these cases. Incorrect computation of this mean flow at the boundary could directly affect the near field physics as well as the far field acoustics. In the present paper, a set of boundary conditions is proposed which focuses on computing the correct mean solution at an artificial boundary, while still maintaining the non-reflecting feature for the outgoing transient and acoustic waves.

Sidewall finite-conductivity effects in confined turbulent thermal convection

2002 ◽  
Vol 473 ◽  
pp. 201-210 ◽  
Author(s):  
ROBERTO VERZICCO
Keyword(s):  
Boundary Conditions ◽  
Thermal Convection ◽  
Lateral Wall ◽  
Finite Conductivity ◽  
Mean Flow ◽  
Number Range ◽  
Additional Heat ◽  
Low Aspect Ratio ◽  
Temperature Boundary ◽  
The Mean

The effects of a sidewall with finite thermal conductivity on confined turbulent thermal convection has been investigated using direct numerical simulation. The study is motivated by the observation that the heat flowing through the lateral wall is not always negligible in the low-aspect-ratio cells of several recent experiments. The extra heat flux modifies the temperature boundary conditions of the flow and therefore the convective heat transfer. It has been found that, for usual sidewall thicknesses, the heat travelling from the hot to the cold plates directly through the sidewall is negligible owing to the additional heat exchanged at the lateral fluid/wall interface. In contrast, the modified temperature boundary conditions alter the mean flow yielding significant Nusselt number corrections which, in the low Rayleigh number range, can change the exponent of the Nu vs. Ra power law by 10%.

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