De novo aortic insufficiency (AI) following continuous flow left ventricular assist device (CF-LVAD) implantation is a common complication. Traditional early management utilizes speed augmentation to overcome the regurgitant flow in an attempt to augment net forward flow, but this strategy increases the aortic transvalvular gradient which predisposes the patient to progressive aortic valve pathology and may have deleterious effects on aortic shear stress and right ventricular (RV) function. We employed a closed-loop lumped-parameter mathematical model of the cardiovascular system including the four cardiac chambers with corresponding valves, pulmonary and systemic circulations, and the LVAD. The model is used to generate boundary conditions which are prescribed in blood flow simulations performed in a three-dimensional (3D) model of the ascending aorta, aortic arch, and thoracic descending aorta. Using the models, impact of various patient management strategies, including speed augmentation and pharmacological treatment on systemic and pulmonary (PA) vasculature, were investigated for four typical phenotypes of LVAD patients with varying degrees of RV to PA coupling and AI severity. The introduction of mild/moderate or severe AI to the coupled RV and pulmonary artery at a speed of 5,500 RPM led to a reduction in net flow from 5.4 L/min (no AI) to 4.5 L/min (mild/moderate) to 2.1 L/min (severe). RV coupling ratio (Ees/Ea) decreased from 1.01 (no AI) to 0.96 (mild/moderate) to 0.76 (severe). Increasing LVAD speed to 6,400 RPM in the severe AI and coupled scenario, led to a 42% increase in net flow and a 16% increase in regurgitant flow (RF) with a nominal decrease of 1.6% in RV myocardial oxygen consumption (MVO2). Blood pressure control with the coupled RV with severe AI at 5,500 RPM led to an 81% increase in net flow with a 15% reduction of RF and an 8% reduction in RV MVO2. With an uncoupled RV, the introduction of mild/moderate or severe AI at a speed of 5,500 RPM led to a reduction in net flow from 5.0 L/min (no AI) to 4.0 L/min (mild/moderate) to 1.8 L/min (severe). Increasing the speed to 6,400 RPM with severe AI and an uncoupled RV increased net flow by 45%, RF by 15% and reduced RV MVO2 by 1.1%. For the uncoupled RV with severe AI, blood pressure control alone led to a 22% increase in net flow, 4.2% reduction in RF, and 3.9% reduction in RV MVO2; pulmonary vasodilation alone led to a 18% increase in net flow, 7% reduction in RF, and 26% reduction in RV MVO2; whereas, combined BP control and pulmonary vasodilation led to a 113% increase in net flow, 20% reduction in RF and 31% reduction in RV MVO2. Compared to speed augmentation, blood pressure control consistently resulted in a reduction in WSS throughout the proximal regions of the arterial system. Speed augmentation to overcome AI in patients supported by CF-LVAD appears to augment flow but also increases RF and WSS in the aorta, and reduces RV MVO2. Aggressive blood pressure control and pulmonary vasodilation, particularly in those patients with an uncoupled RV can improve net flow with more advantageous effects on the RV and AI RF.