Unsteady Incompressible Flow Simulation using Galerkin Finite Elements with Spatial/Temporal Adaptation

A new adaptive technique for the simulation of unsteady incompressible flows is presented. The initial mesh is generated based on a Cartesian grid with spatial decomposition and a simple optimization step to define the boundaries of the domain. This technique is fast and produces a quad-dominant mesh, while preserving the quality of the elements. Adaptive mesh refinement is performed based on the gradient of the vorticity from the previous time step. The time step is controlled and hence adapted using error estimation of the flow variables with respect to time. A Galerkin finite-element discretization is used to generate the nonlinear system corresponding to the Navier-Stokes equations. The solution of the linearized system is carried out using the GMRES method with a least-squares commutator as a preconditioner. Numerical experiments for various test cases illustrate the strength of this new approach.