Simulation of unsteady incompressible flows using temporal adaptation and dynamic remeshing

An implicit finite-element flow solver based on the Galerkin finite-element method is employed to study unsteady laminar flow past single and multiple objects. A fast dynamic remeshing technique is used to control the distribution of the mesh nodes during the unsteady simulation, thus minimizing (or even eliminating) the need for adding artificial dissipation terms. The quad-dominant mesh generator coupled with this solver is based on a Cartesian mesh with a conforming spatial decomposition. The dynamic remeshing technique preserves the quality of the elements during the refinement/coarsening process. A mixed Galerkin finite-element discretization is used to generate the nonlinear system corresponding to the Navier-Stokes equations. After approximating the time derivative by means of finite differences and applying Picard’s iteration, one obtains linear systems of equations that need to be solved at each time step. The GMRES method combined with a least-squares commutator as a preconditioner is employed for the solution of these linear systems. The time step is controlled and adapted using an error estimation of the computed flow variables with respect to time. Results of several numerical simulations are presented and validated against experimental and numerical studies to demonstrate the viability of this new approach.