The proposed project aims to further develop, assess and analyse numerical algorithms leading to reduction in spurious diapycnal mixing in ocean circulation models. This goal will be achieved by means of the following three measures: (i) the design and implementation of vertical mesh motion algorithms that reduce spurious mixing for a set of dynamical regimes; (ii) use of advective schemes with isopycnal diffusion and design of limiters which are 'aware of diapycnal mixing', keeping it at minimum compatible with TVD character; (iii) development and analysis of high-order advection algorithms relying on high-order flux evaluation by generalised Godunov methods, termed ADER, in combination with kernel-based WENO reconstruction for structured and unstructured meshes. The resulting algorithms will be tested in a combined manner within GETM, and their most promising combinations will be implemented in FESOM (or its follow-up) and ICON-ocean, in the frame of project S2.