Pseudospectral Technique Research Articles

Numerical solution of natural convection in eccentric annuli

The governing equations for transient natural convection in eccentric annular space are solved with two highorder accurate numerical algorithms. The equation set is transformed into bipolar coordinates and split into two one-dimensional equations: finite elements are used in the direction normal to the cylinder surfaces; the pseudospectral technique is used in the azimuthal direction. Transient solutions of the entire flowfield are obtained for 102 </?a<106, 0.70<Pr<102, with the inner cylinder near the top, bottom, and side of the outer cylinder. Results are similar to experimental and numerical values previously published for low Ra numbers. A B c D e g

A pseudo-spectral FFT technique for non-periodic problems

A technique is developed for the use of pseudo-spectral Fast Fourier Transform methods for non-periodic time-dependent problems in fluid dynamics. Called “reduction to periodicity,” it involves the evaluation of a polynomial function which approximates the departure from smooth periodicity of the dependent variable distribution at each time level. The FFT is then applied to the residual distribution. The accuracy is demonstrated in several one-dimensional problems. Stability and iterative convergence are demonstrated in one-dimensional problems with first order, second order, and fourth order time differencing, and in two-dimensional problems with first-order time differencing.

Residual Flow and Boundary Shear Stress in the Turbulent Bottom Layer Beneath Waves

A model is considered of the turbulent bottom boundary layer beneath waves. Closure is effected at the level of the turbulent energy equation and numerical solutions are obtained by a combination of finite-difference methods and a pseudo-spectral technique. These solutions are used to evaluate the induced streaming motion and the boundary shear stress. An expression is derived for the friction coefficient in terms of the bottom roughness and this is found to agree with values reported in experimental studies.