This MSc thesis is centred around better capturing the physics of Navier-Stokes flow problems with the following two CFD methods that preserve integral invariants. A recent 2D mass, kinetic energy, enstrophy and total vorticity conserving (MEEVC) method is the cornerstone of this work. It was constructed with mimetic concepts in mind and its favourable properties were a reason to use it as inspiration for developing a novel 3D mass, kinetic energy and helicity conserving (MEHC) method. This method has a separate equation for the evolution of helical density in its formulation, a feature which is possibly unique in CFD.