A technical problem in the calculation of laminar flow near irregular surfaces described by sampled geometric data

The numerical simulation of fluid flow and transport near biological surfaces must take into account the natural irregularity of these surfaces if the influence of the surface geometry on the near-wall flow field is to be modeled. If the geometric description of a biological surface has a limited resolution, what impact will this have on the accuracy of a computional simulation of the near-wall flow field? It is important to emphasize here that the problem arises from the limited number of data points describing the geometry and not from any limit on the number of mesh points in any subsequent calculation. In this note we show that if every point in a geometric data set describing an axisymmetric model of a diseased coronary artery is taken as a mesh point, then a well converged and otherwise accurately calculated wall shear stress distribution contains a degree of uncertainty which is attributable wholly to the limited resolution of the original geometric model. The approach taken is to repeat the numerical calculation on a reduced resolution version of the original geometric data set, comparing the wall shear stress distribution with that obtained originally. We conclude that accurate computational modeling and simulation of transport processes near irregular biological surfaces will be highly dependent on the availability of well-resolved geometric data describing the surface under study.