Finite difference method

Abstract: Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.

Abstract: An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization The momentum equation is discretized in vector form, thus avoiding problems near the poles The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data A resolution of 16 levels in the vertical is used, with various horizontal resolutions The model is found to be stable and efficient, and to give realistic output fields Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable

Abstract: Several improvements to the finite-difference time-domain (FDTD) method for calculating the radar cross section (RCS) of a perfectly conducting target are presented. Sinusoidal and pulsed FDTD excitations are compared to determine an efficient method of finding the frequency response of targets. The maximum cell size, the minimum number of external cells, and a method to eliminate field storage in the shielded internal volume of perfect conductors to reduce the computer storage requirements of FDTD are discussed. The magnetic-field DC offset induced by surface currents on perfectly conducting objects is observed, and its effects are removed by postprocessing to achieve convergence of the RCS calculations. RCS calculations using the FDTD method in two dimensions are presented for both square and circular infinite cylinders illuminated by both transverse electric and transverse magnetic polarized plane waves. The RCS of a metal cube in three dimensions is also presented. Good agreement between FDTD calculations and theoretical values was achieved for all cases, and parameters necessary to achieve this agreement are examined. >