Conservative unsteady simulation of arbitrary motion in two-dimensional spacetime using central difference, upwind and hybrid formulations

A spacetime framework is presented to solve unsteady aerodynamics problems as an alternative to conventional approaches for complex problems involving large deformation or topological change such as store separation, slat and flap deployment or spoiler deflection. It avoids complex CFD meshing methods, such as Chimera, by the use of a finite-volume approach both in space and time. The
use of a central-difference scheme in the time direction yields non-physical transient solutions as a consequence of pressure waves travelling backwards in time. Therefore, an upwind formulation is provided and validated against one-dimensional test cases: a semi-infinite piston and a finite piston with a sharp change in direction. Also a hybrid formulation is given and several two-dimensional unsteady aerodynamics cases are computed with all three formulations and compared, demonstrating that the use of an upwind time stencil yields more representative physical solutions and improves the rate of convergence. In particular, the following problems are presented: a pitching NACA-0012 (periodic); a simple flap deflection; a spoiler deployment; a full landing case with a combination of slat, flap and spoiler deployments along with ground effect; and a case where aerofoils fly in opposite directions at subsonic and supersonic speeds.