CFD simulation of arbitrary motion in two-dimensional spacetime using cut-cell meshes

Arbitrary unsteady motion demands a method that allows connectivity to change in time, whilst preserving accuracy and conservation. To achieve this, a mesh can be constructed in time as well as space, and this allows total flexibility; there are no restrictions on the type of motions that may be included, and the problem of mesh motion is replaced by mesh generation. Such a ‘space-time’ solver has been developed by the authors, and validated previously for a pitching aerofoil case. To extend this method, and make it applicable to entirely general problems, a cartesian cut-cell method has been developed, and is demonstrated here for creating space-time meshes in three dimensions, allowing arbitrary unsteady motion in two dimensions. This is demonstrated for cases involving aerofoils flying through a mesh and past obstacles in close proximity, which is accomplished in a fully conservative manner and to a level of accuracy consistent with what any equivalent steady simulation would be able to achieve.