A Novel Computational Framework for Pulsatile Wall-shear Stress in Image-based Computational Fluid Dynamics

Wall shear stress (WSS), a tangential force per unit area exerted on the inner wall of a vessel by blood flow, plays an important role in the prevention, pathogenesis, and treatment of cardiovascular diseases. Image-based computational fluid dynamics provides a unique tool to quantify the velocity vector field, from which WSS is conventionally calculated via finite difference method. The key is to determine the local normal direction of the wall in image-based flow domains. We present a novel computation method seamlessly integrating the quantifications of the normal vector \textbf{\textit{n}} of the local wall via signed distance field and the en-route viscous stress tensor $\sigma $ using volumetric lattice Boltzmann method. The WSS is calculated by \begin{figure}[htbp] \centerline{\includegraphics[width=1.56in,height=0.18in]{020820201.eps}} \label{fig1} \end{figure} (Einstein index notation). An application study is to quantify WSS of Womersley flow in ducts. The computational efficiency and accuracy are assessed via comparisons with analytical solutions. The effects of Reynolds number, Womersley number, and shape of cross-section on WSS are systematically explored.