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The subtle interplay between multiple physics, often coupled to the presence of interfaces and happening at various length scale, is responsible for the remarkable properties of complex fluids. Numerically it makes them extremely challenging to simulate. The numerical approach I will present in this talk is built around our incompressible fluid solver on adaptive Octree/Quadtree grids, which are highly effective in capturing different length scales. Designed as a stable projection method, where the viscous effects are treated implicitly, it was shown to be unconditionally stable. Recently this solver was extended to simulate non-miscible two phase flows. In this novel approach, the interface and continuity equations are treated in sharp manner and by using a modified pressure correction projection method, we were able to alleviate the standard time step restriction incurred by capillary forces. As we will see these properties make our framework a robust tool to simulate challenging single and two phase flows problems. I will then focus on one specific type of complex fluids: confined active suspensions, of which a bath swimming microorganism is paradigmatic example. I will detail how our simulation engine was used to model such flows, and present some numerical examples. Specifically we will see how the collective behavior and spontaneous flowing states can emerge from the hydrodynamics interactions between swimmers, and how this dynamic can be controlled by the confining geometry.