In recent years, transcatheter aortic valve replacement (TAVR) has become the leading method for treating aortic stenosis. While the procedure has improved dramatically in the past decade, there are still uncertainties about the impact of TAVR on coronary blood flow. Recent research has indicated that negative coronary events after TAVR may be partially driven by impaired coronary blood flow dynamics. Furthermore, the current technologies to rapidly obtain non-invasive coronary blood flow data are relatively limited. Herein, we present a lumped parameter computational model to simulate coronary blood flow in the main arteries as well as a series of cardiovascular hemodynamic metrics. The model was designed to only use a few inputs parameters from echocardiography, computed tomography and a sphygmomanometer. The novel computational model was then validated and applied to 19 patients undergoing TAVR to examine the impact of the procedure on coronary blood flow in the left anterior descending (LAD) artery, left circumflex (LCX) artery and right coronary artery (RCA)and various global hemodynamics metrics. Based on our findings, the changes in coronary blood flow after TAVR varied and were subject specific (37% had increased flow in all three coronary arteries, 32% had decreased flow in all coronary arteries, and 31% had both increased and decreased flow in different coronary arteries). Additionally, valvular pressure gradient, left ventricle (LV) workload and maximum LV pressure decreased by 61.5%, 4.5% and 13.0% respectively, while mean arterial pressure and cardiac output increased by 6.9% and 9.9% after TAVR. By applying this proof-of-concept computational model, a series of hemodynamic metrics were generated non-invasively which can help to better understand the individual relationships between TAVR and mean and peak coronary flow rates. In the future, tools such as these may play a vital role by providing clinicians with rapid insight into various cardiac and coronary metrics, rendering the planning for TAVR and other cardiovascular procedures more personalized.