Adaptive Implicit Explicit Finite-Element Algorithms For Fluid-Mechanics Problems

The adaptive implicit-explicit (AIE) approach is presented for the finite element solution of various problems in computational fluid mechanics. In the AIE approach the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that with this approach substantial savings in the CPU time and memory can be achieved.