UNSTEADY TRANSONIC 2-DIMENSIONAL EULER SOLUTIONS USING FINITE-ELEMENTS

A finite element solution of the unsteady Euler equations is presented, and demonstrated for two-dimensional airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage Runge-Kutta scheme to march forward in time. Triangular finite elements are employed in an unstructured O-mesh computational grid surrounding the airfoil. Grid points are fixed in space at the far-field boundary and are constrained to move with the airfoil surface to form the near-field boundary. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid-body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite volume techniques. The effects of using either a lumped or consistent mass matrix were studied and are presented. Results show the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils.