Conservative unsteady simulation of arbitrary boundary deformation using spacetime meshes

Simulation of unsteady fluid motion with arbitrary boundary motion or topological change remains restricted due to mesh motion limitations, especially if numerical conservation is required. This work presents an updated interpretation of the fluid conservation laws in space and time that leads to a mesh philosophy that unifies space and time. This effectively replaces the problem of mesh motion with the problem of mesh generation, and since connectivity is no longer constant in time any motion or topological change may be simulated. Examples are given applying the method to a standard pitching aerofoil test case and an appearing/disappearing object to validate and then demonstrate the capability of the method. Results for the pitching case are accurate, and the appearing/disappearing object shows qualitatively correct behaviour.