Ocean/sea-ice simulation models are widely used in realistic contexts for climate studies (coupled to the atmosphere) and for the study of the atmospherically-forced ocean general circulation, and in more simplified contexts for investigating isolated processes (e.g. idealized test-cases). Thanks to advances in computational power, those models are now configured with increasingly higher horizontal/vertical resolution which requires continuous rethinking of numerical methods and modeling assumptions. The objective of this session is to bring together scientists working on the improvement/development of numerical kernels of ocean/sea-ice models (and/or simplified models like transport or shallow-water equations), including their synergy with physical parameterizations. The scope is on the design, testing, and application of new numerical methods, and the assessment of methods currently used in existing state-of-the-art models in realistic or idealized configurations. This includes three main topics (i) horizontal/vertical discretization techniques adapted to fixed/variable structured/non-structured meshes, and the associated time-integration techniques, (ii) the adaptation of numerical methods to physical constraints : monotonic/positive-definite schemes for passive tracers, the control of numerically-induced mixing, and more generally physics-dynamics coupling issues, (iii) the development of semi-idealized test-cases and/or realistic configurations to exploring the merits of different numerical approaches and highlighting successes, deficiencies or biases in model code, approximations or parameterizations.