Direct numerical simulation is performed to study compressible, viscous flow around a circular cylinder. The present study considers two-dimensional, shock-free continuum flow by varying the Reynolds number between 20 and 100 and the freestream Mach number between 0 and 0.5. The results indicate that compressibility effects elongate the near wake for cases above and below the critical Reynolds number for two-dimensional flow under shedding. The wake elongation becomes more pronounced as the Reynolds number approaches this critical value. Moreover, we determine the growth rate and frequency of linear instability for cases above the critical Reynolds number. From the analysis, it is observed that the frequency of the Bénard-von Kármán vortex street in the time-periodic, fully-saturated flow increases from the dominant unstable frequency found from the linear stability analysis as the Reynolds number increases from its critical value, even for the low range of Reynolds numbers considered. We also notice that the compressibility effects reduce the growth rate and dominant frequency in the linear growth stage. Semi-empirical functional relationships for the growth rate and the dominant frequency in linearized flow around the cylinder in terms of the Reynolds number and freestream Mach number are presented.

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A computational tool is developed for simulating the dynamic response of the human cardiovascular system to various stressors and injuries. The tool couples 0-dimensional models of the heart, pulmonary vasculature, and peripheral vasculature to 1-dimensional models of the major systemic arteries. To simulate autonomic response, this multiscale circulatory model is integrated with a feedback model of the baroreflex, allowing control of heart rate, cardiac contractility, and peripheral impedance. The performance of the tool is demonstrated in 2 scenarios: neurogenic hypertension by sustained stimulation of the sympathetic nervous system and an acute 10% hemorrhage from the left femoral artery.

As animal models fall out of favor, there is demand for simulators to train medical personnel in the management of trauma and hemorrhage. Realism is essential to the development of simulators for training in the management of trauma and hemorrhage, but is difficult to achieve because it is difficult to create models that accurately represent bleeding organs. We present a simulation platform that uses real-time mathematical modeling of hemodynamics after hemorrhage and trauma and visually represents the injury described by the model. Using patient-specific imaging, 3D-mesh representations of the liver were created and merged with an anatomically accurate vascular tree. By using anatomically accurate representations of the vasculature, we were able to model the cardiovascular response to hemorrhage in a specific artery. The incorporation of autonomic tone allowed for the calculation of bleeding rate and aortic pressures. The 3D-mesh representation of the liver allowed us to simulate blood flow from the liver after trauma. For the first time, we have successfully incorporated tissue modeling and fluid dynamics with a model of the cardiovascular system to create a simulator. These simulations may aid in the creation of realistic virtual environments for training.

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