3. Fluid Solver - The Euler System on a Moving Domain

The unsteady aerodynamic forces are computed by solving the system of equations for inviscid compressible flow, i.e. the Euler equations. Introducing the Navier-Stokes system increases the physical damping of the system but increases the computational complexity with appropriate turbulence modelling, and the delicate problem of moving shock wave-boundary layer interactions. The global efforts can be reasonably estimated by the inviscid part of the aerodynamic forces and moments.

The moving and deforming structural boundary implies that the fluid equations now need to be written on a moving domain. For this, the Arbitrary Lagrange Euler formulation, [DON 82] is adopted. The computational domain, denoted by ?, is now also time dependent ?( t), and the boundary is denoted by ??( t), denotes the outward normal of the domain. This requires that the numerical formulation of the Euler equations be verified for the moving cells of volume which discretise the domain ?( t). The accuracy of the numerical method in time will now depend on consistency arguments in time also for the geometrical quantities. This is known as the Discrete Geometric Conservation Law, and needs to be enforced when moving meshes are present, [FAR 98a].

The continuous system of the Euler equations on a moving domain are given by [4]. In two spatial dimensions the state vector is = ( ?, ?u, ?v, ?E) ^T and...