Idempotent filtering in spectral and spectral element methods

The comparison of numerical results for implicit-explicit and fully explicit Runge-Kutta time integration methods for a nozzle flow problem shows that filtering can significantly degrade the accuracy of the numerical solution for long-time integration problems. We demonstrate analytically and numerically that filtering-in-time errors become additive for parallel to u(N)(x, t + k Delta t) - u(N)(x, t)parallel to < parallel to u(N)(x, t)parallel to when nonidempotent filters are used, and suggest the development and implementation of idempotent filters. (c) 2006 Elsevier Inc. All rights reserved.