Patient-specific computational fluid-dynamics (CFD) can assist the clinical decision-making process for Type-B aortic dissection (AD) by providing detailed information on the complex intra-aortic haemodynamics. This study presents a new approach for the implementation of personalised CFD models using non-invasive, and oftentimes minimal, datasets commonly collected for AD monitoring. An innovative way to account for arterial compliance in rigid-wall simulations using a lumped capacitor is introduced, and a parameter estimation strategy for boundary conditions calibration is proposed. The approach was tested on three complex cases of AD, and the results were successfully compared against invasive blood pressure measurements. Haemodynamic results (e.g. intraluminal pressures, flow partition between the lumina, wall shear-stress based indices) provided information that could not be obtained using imaging alone, providing insight into the state of the disease. It was noted that small tears in the distal intimal flap induce disturbed flow in both lumina. Moreover, oscillatory pressures across the intimal flap were often observed in proximity to the tears in the abdominal region, which could indicate a risk of dynamic obstruction of the true lumen. This study shows how combining commonly available clinical data with computational modelling can be a powerful tool to enhance clinical understanding of AD.