Flutter prediction by an Euler method on non-moving Cartesian grids with gridless boundary conditions

A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is implemented for the treatment of surface boundary conditions. For steady flows, the gridless method applies surface boundary conditions using a weighted average of the flow properties within a cloud of nodes in the vicinity of the surface. The weighting is established with shape functions derived using a least-squares fitting of the surrounding nodal cloud. For unsteady calculations, a perturbation of the shape functions is incorporated to account for a fluctuating surface normal direction. The nature of the method provides for efficient and accurate solution of transient flow problems in which surface deflections are small (i.e. flutter calculations) without the need for a deforming mesh. Although small deviations in angle of attack are considered, the mean angle of attack can be large. Results indicate good agreement with available experimental data for unsteady flow, and with computational results addressing flutter of the Isogai wing model obtained using traditional moving mesh algorithms.