Solvers for coupled multi-scale (multi-physics) may be constructed by coupling an array of existing and well tested parallel numerical solvers, each designed to tackle a problem at different spatial and temporal scale. Each solver can be optimized/designed for different computer architecture. Future supercomputers may be composed of heterogeneous processing units, i.e., CPU/GPU. To make an efficient use of computational recourses, the coupled solvers must support topology-aware mapping of tasks to the processing units were the best parallel efficiency could be achieved. Arterial blood circulation is a multi-scale process where time and space scales range from nanoseconds (nanometers) to seconds (meters), reciprocally. The macro-vascular scales describing the flow dynamics in larger vessels are coupled to the meso-vascular scales unfolding dynamics of individual blood cells. The meso- vascular events are coupled to the micro-vascular ones accounting for blood perfusion, clot formation, adhesion of the blood cells to the arterial walls, etc. Besides the multi-scale nature of the problem, its size often presents a substantial computational challenge even for simulations considering a single scale. In this talk we will try to envision the design of a multi-scale solver for blood flow simulations, tailored to heterogeneous computer architecture.