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Wave equation in cylindrical and spherical coordinates

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Proceedings Papers

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005
Paper Number: SEG-2005-0316
... involved plane wave particle motion reflection coefficients given by Zoeppritz s equations and the Weyl/Sommerfeld integral for computing isotropic spherical-wave potentials. Plane-wave particle motion reflection coefficients for VTI media have been presented by Graebner (1992) and in refined form by...
Proceedings Papers

Paper presented at the The Second International Offshore and Polar Engineering Conference, June 14–19, 1992
Paper Number: ISOPE-I-92-260
... introduced in estimation of wave forces. The number of researches conducted on the diffraction force acting on the spherical structure is less than that on the cylindrical structures. Havelock (1954) discussed the diffraction force acting 316 on a submerged sphere under deep water wave condition. His theory...
Journal Articles
International Journal of Offshore and Polar Engineering 3 (01).
Paper Number: ISOPE-93-03-1-007
Published: 01 March 1993
..., the Morisontype equation becomes less accurate and the diffraction theory should be introduced in the estimation of wave forces. The amount of research conducted on the diffraction force acting on the spherical structure is less than that conducted on the cylindrical structures. Havelock (1954...
Proceedings Papers

Paper presented at the The 30th International Ocean and Polar Engineering Conference, October 11–16, 2020
Paper Number: ISOPE-I-20-1133
... ABSTRACT In this paper, we instigate numerically the performance of an oblate spheroidal heaving Wave Energy Converter (WEC). The diffraction/radiation problems are solved in the frequency domain by utilizing the conventional boundary integral equation method. This method is, initially...
Proceedings Papers

Paper presented at the The 30th International Ocean and Polar Engineering Conference, October 11–16, 2020
Paper Number: ISOPE-I-20-3245
... located in the geometric center of the tanks, the first wave probe 1 is placed on the plane = 0 of the semi-spheroid located in the < 0 half of the tank, it departs and ends on the smoothing edge between the semi- spheroid and the circular cylindrical center body. The probe 2 cuts the plane...
Proceedings Papers

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019
Paper Number: SEG-2019-3214725
...-250 . Teixeira , F. L. , and W. C. , Chew , 1997 , PML-FDTD in cylindrical and spherical grids : IEEE Microwave and Guided Wave Letters , 7 , 285 – 287 , doi: 10.1109/75.622542 . Elastic reverse time migration in irregular tunnel environment based on polar coordinate...
Proceedings Papers

Paper presented at the ISRM International Symposium - 8th Asian Rock Mechanics Symposium, October 14–16, 2014
Paper Number: ISRM-ARMS8-2014-091
... observable. Thus, blasting design tends to be based on empirical knowledge or law. It is also well known that fracturing process envisioned here depends on the applied pressure wave forms characterized by such as detonation property and amount of applied explosive. These in turn make the design optimization...
Proceedings Papers

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020
Paper Number: SEG-2020-3406423
... equation 2, the general where M is a 4×4 matrix and b and b are 4×1 vectors; For solution for the potentials of in equation 3 in the -k plane wave incidence, their expressions are given in domain can be written as (Tang and Cheng, 2004; Tang et Schoenberg (1986) and Peng (1994). For the spherical al...
Journal Articles
Journal of Ship Research 16 (01): 41–46.
Paper Number: SNAME-JSR-1972-16-1-41
Published: 01 March 1972
... spheroidal singularity point singularity singularity spheroid coordinate system equation Havelock Water Wave Singularities in a Prolate Spheroidal Coordinate System' By J. N . Newman 2 Singular velocity potentials are derived which satisfy the linear free-surface boundary condition and appropriate...
Proceedings Papers

Paper presented at the The Second International Offshore and Polar Engineering Conference, June 14–19, 1992
Paper Number: ISOPE-I-92-393
... kg Trimonlte charge In an off-centre position, generating a peak pressure of 24 MPa. To minimise the excessive CPU demand a single symmetry is assumed and only half the system modelled. As the charge Is detonated off centre and because the resulting pressure wave travels with a finite velocity, the...
Proceedings Papers

Paper presented at the SPE Unconventional Resources Conference, April 1–3, 2014
Paper Number: SPE-168997-MS
... reflection of the ‘pressure wave’ at the high permeability contrast boundaries was neglected in the previous studies because the amplitude of the reflected waves decays exponentially. A more rigorous treatment including the reflected amplitude into the formulation will be more complicated. However, previous...
Proceedings Papers

Paper presented at the The 30th International Ocean and Polar Engineering Conference, October 11–16, 2020
Paper Number: ISOPE-I-20-3243
... stability among different SPH schemes is made, and the improved SPH method was used to study the nonlinear sloshing. Studies have indicated that models based on Boussinesq-type equations are an effective tool in predicting the behavior of nonlinear waves in coastal and offshore environments and may be used...
Proceedings Papers

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5853357
... plates, etc.) accurately; 5) no linear system needs to be solved for ghost zone wavefield estimation, thus avoiding the singularity issue in a matrix inversion. Conventional Finite-Difference vs. IBFD Method The acoustic wave propagation equations are as follows: qp j jp v fv (1) where p is the...
Proceedings Papers

Paper presented at the The 29th International Ocean and Polar Engineering Conference, June 16–21, 2019
Paper Number: ISOPE-I-19-005
... from the empty tank data). Two different geometries are considered: a hemispherical-bottomed buoy; and a cylindrical structure with a moon-pool (Figure 1). For both structures, the effect of wave steepness on the motion of the structure, along with the load in the mooring, is examined. tank data...
Journal Articles
International Journal of Offshore and Polar Engineering 30 (01): 70–77.
Paper Number: ISOPE-20-30-1-070
Published: 01 March 2020
... moment of inertia, and ID is the case ID number. Table 1 Mass properties for the WECs: Case 1 is for the hemi- spherical-bottomed cylinder in focused wave groups, and Case 2 is the hollow cylinder with a moonpool in focused wave groups Case A [m] Tp [s] Hs [m] h [m] kpA 1 0.20 2.5 0.274 3.00 0.1287 2...
Proceedings Papers

Paper presented at the The Fourteenth International Offshore and Polar Engineering Conference, May 23–28, 2004
Paper Number: ISOPE-I-04-005
... introduced, in accordance with Equations (20) and (21), to express the incident wave in the coordinate system of body q. We note, that the present method has been also used in the past (Mavrakos et al., 1997a, 1997b) to assess the hydrodynamic characteristics of arrays of offshore wave energy converters. In...
Journal Articles
Journal of Ship Research 33 (04): 318–325.
Paper Number: SNAME-JSR-1989-33-4-318
Published: 01 December 1989
... design of a submersible hull [6]. In the second phase, the structures are verified and opti- mized using direct procedures generally based on numerical methods. Submarine strength ulls are generally constructed using cylindrical shells for central sections and spherical shells for head domes. Because of...
Journal Articles
International Journal of Offshore and Polar Engineering 18 (01).
Paper Number: ISOPE-08-18-1-043
Published: 01 March 2008
... circumferential wave number n for half- filled and fully filled cylindrical containers, respectively. From these figures, it can be seen that the present RD element results are in agreement with results obtained by Xi et al. (1997), using a semi-analytical procedure. In particular, for a given circumfer- ential...
Proceedings Papers

Paper presented at the Offshore Technology Conference, April 21–23, 1970
Paper Number: OTC-1209-MS
... upstream end of the diaphragm, a results of this type of analysis agrees distance of 12.0 in. from the coupling point. accurately with the other experiments conducted h additional 0.635 millisec is required for with different geometries. Thus, one can the spherical diverging wave to reach the correctly...
Proceedings Papers

Paper presented at the 1988 SEG Annual Meeting, October 30–November 3, 1988
Paper Number: SEG-1988-0672
... McGowan (1986) have developed a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks. P z,P) = 2Jdp (p2-pr2) -112, J 1: dr l e 0 0 [U(ztp r,r,O)tU(T-p r,r,O)] (2) where U is the wave field, r is the offset in cylindrical coordinates, 7 is the intercept ime p is the ray...

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