Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

The Navier-Stokes equations with both periodic and non-slip boundary condit ions are solved using a new class of wavelets based on distributed approxim ating functionals (DAFs). Extremely high accuracy is found in our wavelet-D AF integration of the analytically solvable Taylor problem, using 32 grid p oints in each of the two spatial dimensions, for Reynolds numbers from Re = 20 to Re = infinity. The present approach is then applied to the lid-drive n cavity problem with. standard non-slip boundary conditions. Physically re asonable solutions are obtained for Reynolds numbers as high as 3200, using 63 grid points in each spatial dimension. Our results indicate that wavele t methods are readily applicable to those dynamical problems for which the existence of possible singularities demands highly accurate solution method s. (C) 1998 Elsevier Science B.V.