The achievements of modern research and their rapid progress from theory to application are increasingly underpinned by computation. Computational approaches are often hailed as a new third pillar of science - in addition to empirical and theoretical work. While its breadth makes computation almost as ubiquitous as mathematics as a key tool in science and engineering, it is a much younger discipline and stands to benefit enormously from building increased capacity and increased efforts towards integration, standardization, and professionalism. The development of new ideas and techniques in computing is extremely rapid, the progress enabled by these breakthroughs is enormous, and their impact on society is substantial: modern technologies ranging from the Airbus 380, MRI scans and smartphone CPUs could not have been developed without computer simulation; progress on major scientific questions from climate change to astronomy are driven by the results from computational models; major investment decisions are underwritten by computational modelling. Furthermore, simulation modelling is emerging as a key tool within domains experiencing a data revolution such as biomedicine and finance. This progress has been enabled through the rapid increase of computational power, and was based in the past on an increased rate at which computing instructions in the processor can be carried out. However, this clock rate cannot be increased much further and in recent computational architectures (such as GPU, Intel Phi) additional computational power is now provided through having (of the order of) hundreds of computational cores in the same unit. This opens up potential for new order of magnitude performance improvements but requires additional specialist training in parallel programming and computational methods to be able to tap into and exploit this opportunity. Computational advances are enabled by new hardware, and innovations in algorithms, numerical methods and simulation techniques, and application of best practice in scientific computational modelling. The most effective progress and highest impact can be obtained by combining, linking and simultaneously exploiting step changes in hardware, software, methods and skills. However, good computational science training is scarce, especially at post-graduate level. The Centre for Doctoral Training in Next Generation Computational Modelling will develop 55+ graduate students to address this skills gap. Trained as future leaders in Computational Modelling, they will form the core of a community of computational modellers crossing disciplinary boundaries, constantly working to transfer the latest computational advances to related fields. By tackling cutting-edge research from fields such as Computational Engineering, Advanced Materials, Autonomous Systems and Health, whilst communicating their advances and working together with a world-leading group of academic and industrial computational modellers, the students will be perfectly equipped to drive advanced computing over the coming decades.