Curved Boundary Research Articles

Accuracy and grid convergence of wall shear stress measured by lattice Boltzmann method

Based on a two-dimensional Poiseuille and Wormersley flow, accuracy and grid convergence of velocity, shear stress and wall shear stress (WSS) measurements were investigated using the single-relaxation-time (SRT) and multiple-relaxation-time (MRT) lattice Boltzmann models under various open and wall boundary conditions. The results showed that grid convergence of shear stress and WSS are not consistent with that of velocity when flow channels are not aligned to the grids, and strongly rely on the used wall boundary conditions. And the MRT model is slightly superior to the SRT when simulating the complicated border flow. Moreover the WSS should be approximately calculated on the fluid nodes closest to walls under the curved boundary (CB) condition but not for the bounce-back (BB) boundary scheme. As applications, distributions of WSS in a wavy-walled channel and distensible carotid artery were simulated which would much more depend on local roughness of vessel intima than channel diameters.

Effects of blood flow, curved boundary and environmental conditions on temperature distribution in a two dimensional model of human skin and subcutaneous tissues.

A mathematical model for the study of the effects of blood flow, metabolic heat production, various environmental conditions and the presence of a curved boundary on the temperature distribution (TD) in a two dimensional model of human skin and subcutaneous tissues (SST) is presented. Based on physiological properties, the interfaces between epidermis-dermis (IED) and dermis-subcutaneous tissues (IDS) have been considered to be irregular and the regions of these layers have been divided into 109 triangular elements of various sizes which are connected with each other by 70 nodes. The results computed from this thermobiological mathematical model, using Galerkin's finite element technique, have been exhibited graphically. The effects of various environmental conditions, blood flow and metabolic heat production are found to be nonuniform on TD at the nodes situated at the same depth in SST. This nonuniformity in TD almost disappears at the nodes situated in dermis nearest to IDS except for the two of the six combinations, considered in the present study, in which highest values of blood flow and metabolic heat production have been considered. The rate of fall of temperature with respect to thickness (towards the skin surface) is higher at the straight boundary (SB) than at the curved boundary (CB). The temperature increases with respect to width (from SB to CB) in epidermis and dermis but decreases in subcutaneous tissues. This increase or decrease of temperature is more pronounced at the nodes situated near to, or at CB. The trend of these temperature profiles in SST reflects the dependence of TD not only on the environmental conditions and biophysical variables but also on the geometry of SST.