Phantoms for dynamic contrast enhanced (DCE) imaging modalities such as DCE computed tomography (DCE-CT) and DCE magnetic resonance imaging (DCE-MRI) are valuable tools for evaluating and comparing imaging systems. It is important for the contrast-agent distribution within the phantom to possess a time dependence that replicates a curve observed clinically, known as the 'tumor-enhancement curve'. It is also important for the concentration field within the lesion to be as uniform as possible. This study demonstrates how computational fluid dynamics (CFD) can be applied to achieve these goals within design constraints. The distribution of the contrast agent within the simulated phantoms was investigated in relation to the influence of three factors of the phantom design. First, the interaction between the inlets and the uniformity of the contrast agent within the phantom was modeled. Second, pumps were programmed using a variety of schemes and the resultant dynamic uptake curves were compared to tumor-enhancement curves obtained from clinical data. Third, the effectiveness of pulsing the inlet flow rate to produce faster equilibration of the contrast-agent distribution was quantified. The models employed a spherical lesion and design constraints (lesion diameter, inlet-tube size and orientation, contrast-agent flow rates and fluid properties) taken from a recently published DCE-MRI phantom study. For DCE-MRI in breast cancer detection, where the target tumor-enhancement curve varies on the scale of hundreds of seconds, optimizing the number of inlet tubes and their orientation was found to be adequate for attaining concentration uniformity and reproducing the target tumor-enhancement curve. For DCE-CT in liver tumor detection, where the tumor-enhancement curve varies on a scale of tens of seconds, the use of an iterated inlet condition (programmed into the pump) enabled the phantom to reproduce the target tumor-enhancement curve within a few per cent beyond about 6 s of wash-in. This time was cut in half by the final CFD-derived strategy of flow pulsing. Driving the pump with a 25% duty cycle pulsatile waveform produced a nearly uniform concentration in the phantom in just a few seconds under typical conditions. Comparisons with published x-ray measurements using tumor-enhancement curves for both benign and malignant breast lesions showed a difference of approximately 4% between the CFD predictions and measurements of the contrast-agent concentration averaged over the lesion volume. The techniques derived using CFD optimization can be used in future phantom designs, including as starting points for future CFD phantom studies employing new lesion geometries and tumor-enhancement curves.