Electroacoustic Sensitivity of Pressure‐Equalized Spherical and Cylindrical Hydrophones

Section 13.7 Cylindrical and Spherical Coordinates

PML-FDTD in Cylindrical and Spherical Grids

Perfectly matched layers (PML’s) are derived for cylindrical and spherical finite-difference time-domain (FDTD) grids. The formulation relies on the complex coordinate stretching approach. Two-dimensional (2-D) cylindrical and three-dimensional (3-D) spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation...

WENO Schemes for Cylindrical and Spherical Grid

In this paper, we apply the high order WENO schemes to uniform cylindrical and spherical grid. Many 2-D and 3-D problems can be solved in 1-D equations if they have angular and radial symmetry. The reduced equations will typically involve geometric source terms. Therefore, conventional numerical schemes for Cartesian grid may not work well. We propose several approaches to apply the high order ...

PML - FDTD in Cylindrical and Spherical GridsF

| Perfectly Matched Layers (PML) are derived for cylindrical and spherical FDTD grids. The formulation relies on the complex coordinate stretching approach. 2D cylindrical and 3D spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation by showing very good agreement between the PML-FDTD results and the fre...

SPH in spherical and cylindrical coordinates

New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH. The Lagrangian formalism is used to derive the corresponding set of modified SPH equations of motion. The results show good agreement both with analytical and numerical results, in the case of the Sod shock tube test, the Noh infinite shock probl...