Single ventricle heart defects, where systemic and pulmonary venous returns mix in the single functional ventricle, represent the most complex form of congenital heart defect, affecting 2 babies per 1000 live births. Surgical repairs, termed "Fontan Repairs," reroute the systemic venous return directly to the pulmonary arteries, thus preventing venous return mixing and restoring normal oxygenation saturation levels. Unfortunately, these repairs are only palliative and Fontan patients are subjected to a multitude of chronic complications. It has long been suspected that hemodynamics play a role in determining patient outcome. However, the number of anatomical and functional variables that come into play and the inability to conduct large scale clinical evaluations, due to too small a patient population, has hindered decisive progress and there is still not a good understanding of the optimal care strategies on a patient-by-patient basis. Over the past decades, image-guided computational fluid dynamics (CFD) has arisen as an attractive option to accurately model such complex biomedical phenomena, providing a high degree of freedom regarding the geometry and flow conditions to be simulated, and carrying the potential to be automated for large sample size studies. Despite these theoretical advantages, few CFD studies have been able to account for the complexity of patient-specific anatomies and in vivo pulsatile flows. In this thesis, we develop an unstructured Cartesian immersed-boundary flow solver allowing for high resolution, time-accurate simulations in arbitrarily complex geometries, at low computational costs. Combining the proposed and validated CFD solver with an interactive virtual-surgery environment, we present an image-based surgical planning framework that: a) allows for in depth analysis of the pre-operative in vivo hemodynamics; b) enables surgeons to determine the optimum surgical scenario prior to the operation. This framework is first applied to retrospectively investigate the in vivo pulsatile hemodynamics of different Fontan repair techniques, and quantitatively compare their efficiency. We then report the prospective surgical planning investigations conducted for six failing Fontan patients with an interrupted inferior vena cava and azygous continuation. In addition to a direct benefit to the patients under consideration, the knowledge derived from these surgical planning studies will also have a larger impact for the clinical management of Fontan patients as they shed light onto the impact of caval offset, vessel flaring and other design parameters upon the Fontan hemodynamics depending on the underlying patient anatomy. These results provide useful surgical guidelines for each anatomical template, which could benefit the global surgical community, including centers that do not have access to patient-specific surgical planning interfaces.