Adaptive Time-Stepping for Incompressible Flow Part II: Navier-Stokes Equations

We outline a new class of robust and efficient methods for solving the Navier-Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach.