Abstract
Simulating cardiovascular flows under healthy and pathological conditions is of primary importance from both engineering and clinical point of views. However, the complexity of the flow conditions and structures in the cardiovascular system constantly requires the use and the development of new numerical strategies. This chapter describes how smoothed particle hydrodynamics (SPH) can be used to simulate cardiovascular flows. SPH is a fully Lagrangian mesh-free method originally developed in the 1970s to simulate astrophysical phenomena and its first terrestrial applications to simulate inviscid flows only started during the early 1990s. In SPH, the physical domain is discretized by a number of particles. Each particle has its own physical properties. Numerical discretization involves approximation of the physical properties of each particle by interpolating the properties of its neighboring particles. This chapter will cover the fundamental concepts, the mathematical formulation, and the implementation of SPH. A set of benchmark cases, relevant to cardiovascular flows, will be introduced for numerical code validations. Finally, some recent applications to cardiovascular flows will be presented highlighting the advantages, the limitations, and the challenges when using SPH.
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