Microfluidic tumour spheroid-on-a-chip platforms enable control of spheroid size and their microenvironment and offer the capability of high-throughput drug screening, but drug supply to spheroids is a complex process that depends on a combination of mechanical, biochemical, and biophysical factors. To account for these coupled effects, many microfluidic device designs and operating conditions must be considered and optimized in a time- and labour-intensive trial-and-error process. Computational modelling facilitates a systematic exploration of a large design parameter space via in silico simulations, but the majority of in silico models apply only a small set of conditions or parametric levels. Novel approaches to computational modelling are needed to explore large parameter spaces and accelerate the optimization of spheroid-on-a-chip and other organ-on-a-chip designs. Here, we report an efficient computational approach for simulating fluid flow and transport of drugs in a high-throughput arrayed cancer spheroid-on-a-chip platform. Our strategy combines four key factors: i) governing physical equations; ii) parametric sweeping; iii) parallel computing; and iv) extensive dataset analysis, thereby enabling a complete âfull-factorialâ exploration of the design parameter space in combinatorial fashion. The simulations were conducted in a time-efficient manner without requiring massive computational time. As a case study, we simulated >15,000 microfluidic device designs and flow conditions for a representative multicellular spheroids-on-a-chip arrayed device, thus acquiring a single dataset consisting of âŒ10 billion datapoints in âŒ95 GBs. To validate our computational model, we performed physical experiments in a representative spheroid-on-a-chip device that showed excellent agreement between experimental and simulated data. This study offers a computational strategy to accelerate the optimization of microfluidic device designs and provide insight on the flow and drug transport in spheroid-on-a-chip and other biomicrofluidic platforms.