Facing energy future is one of the large challenges of the world, with numerous implications for R&D strategy of energy companies. One of the Total R&D missions is the development of competences on advanced technologies, such as Advanced Computing (HPC), Material sciences, Biotechnologies, Nanotechnologies, New analytical techniques, IT Technologies. HPC allows also tackling the challenge in code coupling: both a horizontal direction -multi-physics-, (chemistry and transport, or structural mechanics, acoustics, fluid dynamics, and thermal heat transfer, ...) and in the vertical direction -multi-scale models- (i.e. from continuum to mesoscale to molecular dynamics to quantum chemistry) which requires bridging space and time scales that span many orders of magnitude. This leads to improve at the same time more accurate physical model and numerical methods and algorithms and these improvements of numerical simulations will be illustrated by their application, use and impact in Total strategic activities such as: seismic, depth imaging by solving waves equation; oil reservoir modeling by solving transport, thermal and chemical equations; multi scale process modeling and control, such as slurry loop process; mechanical structures and geomecanics.