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

The Navier-Stokes equations with both periodic and non-slip boundary conditions are solved using a new class of wavelets based on distributed approximating functionals (DAFs). Extremely high accuracy is found in our wavelet-DAF integration of the analytically solvable Taylor problem, using 32 grid points in each of the two spatial dimensions, for Reynolds numbers from Re = 20 to Re = ∞. The present approach is then applied to the lid-driven cavity problem with standard non-slip boundary conditions. Physically reasonable solutions are obtained for Reynolds numbers as high as 3200, using 63 grid points in each spatial dimension. Our results indicate that wavelet methods are readily applicable to those dynamical problems for which the existence of possible singularities demands highly accurate solution methods.