Our study aimed to elucidate the role of different shunts and provide novel insights into optimal treatment approaches for complete transposition of the great arteries (TGA), which is characterized by unique and complicated circulatory dynamics. We constructed a computational cardiovascular TGA model and manipulated cardiovascular parameters, such as atrial septal defect (ASD) and patent ductus arteriosus (PDA) sizes, to quantify their effects on oxygenation and hemodynamics. In addition, ASD flow patterns were investigated as innovative indications for balloon atrial septostomy (BAS). Our model of TGA with an intact ventricular septum (TGA-IVS) showed that a large ASD can achieve sufficient mixing for survival without PDA, and the presence of PDA is detrimental to oxygen delivery. A treatment strategy for TGA-IVS that enlarges the ASD as much as possible by BAS and PDA closure would be desirable. In TGA with a ventricular septal defect (TGA-VSD), the VSD allows for higher oxygenation and reduces the detrimental effects of PDA on systemic circulation. In TGA-VSD, both strategies of enlarging the ASD by BAS with a closed PDA and adjusting the PDA in response to pulmonary vascular resistance (PVR) reduction without BAS may be effective. The simulated ASD flow patterns showed that the sharp peak left-to-right flow pattern in systole (σ-wave) reflected the hemodynamically significant ASD size, independent of PDA, VSD, and PVR. The ASD flow pattern visualized by Doppler echocardiography provides clinical insights into the significance of an ASD and indications for BAS, which are not readily apparent through morphological assessment.NEW & NOTEWORTHY Complete transposition of the great arteries (TGA) represents complex and unique circulation that is dependent on blood mixing through multiple interacting shunts. Consequently, the role of each shunt and the treatment strategy remain unclear. We developed a mathematical model of TGA circulation, revealing the significant influence of atrial septal defect (ASD) on oxygenation and hemodynamics. The blood flow pattern through the ASD reflects its hemodynamic impact and helps determine treatment strategies.