scholarly journals The Performance of the Higher-Order Radiation Condition Method for the Penetrable Cylinder

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Bülent Yilmaz
Keyword(s):  
Total Pressure ◽  
Wave Speed ◽  
Surrounding Medium ◽  
Radiation Condition ◽  
Higher Order ◽  
Two Dimensions ◽  
Total Field ◽  
Condition Method ◽  
Cartesian System ◽  
Total Velocity

We have considered the scattering of a plane wave by a penetrable acoustic circular cylinder. The boundary conditions are continuity of the total pressure and the total velocity. The wave speed and density of the target are different from that of the surrounding medium. We investigated the performance of higher-order SRCs up toL4operator in two dimensions. We assume that in the rectangular Cartesian system of axes,(x,y,z), thezaxis coincides with the axis of the cylinder and an incident wave propagates in a direction perpendicular to thezaxis. All the field quantities are then independent ofz. Numerical results are added to present the change of the module of the total field and the magnitude of the far field with respect toθ.

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

scholarly journals Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

2009 ◽  
Vol 621 ◽  
pp. 215-242 ◽  
Author(s):  
FÉLICIEN BONNEFOY ◽  
MICHAEL H. MEYLAN ◽  
PIERRE FERRANT
Keyword(s):  
Critical Speed ◽  
Moving Boundary ◽  
Moving Load ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Two Dimensions ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Bernoulli’S Equation

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

scholarly journals Sheared free-surface flow over three-dimensional obstructions of finite amplitude

2019 ◽  
Vol 878 ◽  
pp. 740-767
Author(s):  
Andreas H. Akselsen ◽  
Simen Å. Ellingsen
Keyword(s):  
Perturbation Technique ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Radiation Condition ◽  
Finite Amplitude ◽  
Higher Order ◽  
Surface Flow ◽  
Current Profile ◽  
Bottom Boundary Condition ◽  
Lord Kelvin

When shallow water flows over uneven bathymetry, the water surface is modulated. This type of problem has been revisited numerous times since it was first studied by Lord Kelvin in 1886. Our study analytically examines currents whose unperturbed velocity profile $U(z)$ follows a power law $z^{q}$, flowing over a three-dimensional uneven bed. This particular form of $U$, which can model a miscellany of realistic flows, allows explicit analytical solutions. Arbitrary bed shapes can readily be imposed via Fourier’s theorem provided their steepness is moderate. Three-dimensional vorticity–bathymetry interaction effects are evident when the flow makes an oblique angle with a sinusoidally corrugated bed. Streamlines are found to twist and the fluid particle drift is redirected away from the direction of the unperturbed current. Furthermore, a perturbation technique is developed which satisfies the bottom boundary condition to arbitrary order also for large-amplitude obstructions which penetrate well into the current profile. This introduces higher-order harmonics of the bathymetry amplitude. States of resonance for first- and higher-order harmonics are readily calculated. Although the method is theoretically restricted to bathymetries of moderate inclination, a wide variety of steeper obstructions are satisfactorily represented by the method, even provoking occurrences of recirculation. All expressions are analytically explicit and sequential fast Fourier transformations ensure quick and easy computation for arbitrary three-dimensional bathymetries. A method for separating near and far fields ensures computational convergence under the appropriate radiation condition.

Computation of Exterior Acoustics Problems in Two Dimensions by Trefftz-Type Finite Elements

2015 ◽  
Vol 712 ◽  
pp. 17-22
Author(s):  
Małgorzata Stojek
Keyword(s):  
Finite Elements ◽  
Cross Section ◽  
Radiation Condition ◽  
Two Dimensions ◽  
Least Square ◽  
Fe Method ◽  
Complete Set ◽  
Least Square Procedure

The paper deals with the application of the so-called T-type finite elements [1] to the calculation of the exterior acoustic problems in two dimensions. The method is based on the use of asuitably truncated T-complete set of Trefftz functions over individual subdomains linked by means ofa least square procedure. The vertex singularities and the Sommerfeld radiation condition are readilyincorporated in the trial functions. In order to show the performance of the approach two examples ofcomputations for infinite cylinders (of circular and square cross section) are presented and comparedwith those obtained by means of h-adaptive FE method [2].

HIERARCHICAL DIMENSIONS OF COPING STYLES: A STUDY CONDUCTED WITH TURKISH UNIVERSITY STUDENTS

2006 ◽  
Vol 34 (5) ◽  
pp. 525-534 ◽  
Author(s):  
Faruk Gençöz ◽  
Tülin Gençöz ◽  
Özlem Bozo
Keyword(s):  
Factor Analysis ◽  
University Students ◽  
Coping Styles ◽  
Reliability And Validity ◽  
Higher Order ◽  
Two Dimensions ◽  
Good Reliability ◽  
Empirical Examination ◽  
Turkish University Students ◽  
Third Dimension

An empirical examination was carried out of the hierarchical dimensions of coping styles in a Turkish sample. Ways of coping data were collected from 194 university students, subjected to factor analysis and 5 factors were obtained. These factors were subjected to second-order factor analysis which revealed 3 main dimensions. As predicted the first two dimensions were problem-focused coping and emotion-focused coping. The third dimension consisted of items related to seeking social support, implying the presence and importance of an indirect coping style. In addition to construct validity, Guttman split-half reliability and criterion validity of these three higher order factors revealed good reliability and validity outcomes. It was also emphasized that these 3 higher order factors constituted independent dimensions of coping styles. Implications of the results are discussed.

Sign in / Sign up

Export Citation Format

Share Document