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.

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.

Complete Radiation Boundary Conditions for Convective Waves

2012 ◽  
Vol 11 (2) ◽  
pp. 610-628 ◽  
Author(s):  
Thomas Hagstrom ◽  
Eliane Bécache ◽  
Dan Givoli ◽  
Kurt Stein
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Radiation Boundary Condition ◽  
Linearized Euler Equations ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Optimal Efficiency ◽  
Radiation Boundary ◽  
Scalar Equations

AbstractLocal approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

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.

Complete Radiation Boundary Conditions for Maxwell’s Equations

2021 ◽  
Vol 35 (11) ◽  
pp. 1290-1291
Author(s):  
Thomas Hagstrom ◽  
John Lagrone
Keyword(s):  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Numerical Experiments ◽  
Maxwell's Equations ◽  
Arbitrary Order ◽  
Rational Approximants ◽  
Radiation Boundary Condition ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Radiation Boundary

We describe the construction, analysis, and implementation of arbitrary-order local radiation boundary condition sequences for Maxwell’s equations. In particular we use the complete radiation boundary conditions which implicitly apply uniformly accurate exponentially convergent rational approximants to the exact radiation boundary conditions. Numerical experiments for waveguide and free space problems using high- order discontinuous Galerkin spatial discretizations are presented.

RADIATION BOUNDARY CONDITIONS FOR THE HELMHOLTZ EQUATION FOR ELLIPSOIDAL, PROLATE SPHEROIDAL, OBLATE SPHEROIDAL AND SPHERICAL DOMAIN BOUNDARIES

2012 ◽  
Vol 20 (04) ◽  
pp. 1230001 ◽  
Author(s):  
DAVID S. BURNETT
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Computational Domain ◽  
Prolate Spheroidal ◽  
Radiation Boundary Conditions ◽  
Oblate Spheroidal ◽  
Aspect Ratios ◽  
Wide Range ◽  
Radiation Boundary ◽  
Angular Coordinates

One of the most popular radiation boundary conditions for the Helmholtz equation in exterior 3-D regions has been the sequence of operators developed by Bayliss et al.1 for computational domains with spherical exterior boundaries. The present paper extends those spherical operators to triaxial ellipsoidal boundaries by utilizing two mathematical constructs originally developed for ellipsoidal acoustic infinite elements.2 The two constructs are: (i) a radial/angular coordinate system for ellipsoidal geometry, and (ii) a convergent ellipsoidal radial expansion for exterior fields, analogous to the classical spherical multipole expansion. The ellipsoidal radial and angular coordinates are smooth generalizations of the traditional radial and angular coordinates used in spherical, prolate spheroidal and oblate spheroidal systems. As a result, all four coordinate systems and their corresponding radiation boundary conditions are included within this single ellipsoidal system, varying smoothly from one to the other. The geometric flexibility of this system enables the exterior boundary of the computational domain to closely circumscribe objects with a wide range of aspect ratios, thereby reducing the size and cost of 3-D computational models.

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.

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