Thistleton, W. (2016Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational modelReceived: date / Accepted: date Abstract A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines: (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by: (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method we use an exterior calculus based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how
We report on recent results in modeling ocular blood flow (some parts were presented at ARVO 2013 [1]). For this simulations we used discrete exterior calculus based numerical methods. These methods aim to preserve the main features of the original analytical equations and are very suitable for curved surfaces. We will discuss the model and present the numerical methods. We will also give an overview of existing/available segmentation methods to extract the vascular tree from given retina images and our plans how to use them as a front end to our model.
Experimental results for condensation in compact heat exchangers show that the heat transfer due to condensation is significantly better compared to classical heat exchangers, especially when using R134a instead of water as the refrigerant. This suggests that surface tension plays a role. Using generalized dimensional analysis we derive reduced model equations and jump conditions for condensation in a vertical tube with cylindrical cross section. Based on this model we derive a single ordinary differential equation for the thickness of the condensate film as function of the tube axis. Our model agrees well with commonly used models from existing literature. It is based on the physical dimensions of the problem and has greater geometrical flexibility.
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