The computational modelling of DNA is becoming crucial in light of new advances in DNA nano-technology, single-molecule experiments and in vivo DNA tampering. Here we present a mesoscopic model for double stranded DNA (dsDNA) at the single nucleotide level which retains the characteristic helical structure, while being able to simulate large molecules-up to a million base pairs-for time-scales which are relevant to physiological processes. This is made possible by an efficient and highly-parallelised implementation of the model which we discuss here. The model captures the main characteristics of DNA, such as the different persistence lengths for double and single strands, pitch, torsional rigidity and the presence of major and minor grooves. The model constitutes a starting point for the future implementation of further features, such as sequence specificity and electrostatic repulsion. We show that the behaviour of the presented model compares favourably with single molecule experiments where dsDNA is manipulated by external forces or torques. We finally present some results on the kinetics of denaturation of linear DNA and supercoiling of closed dsDNA molecules.