Physical modelling is a sophisticated synthesis technique, often used in the design of Digital Musical Instruments (DMIs). Some of the most precise physical simulations of sound propagation are based on Finite-Difference Time-Domain (FDTD) methods, which are stable, highly parameterizable but characterized by an extremely heavy computational load. This drawback hinders the spread of FDTD from the domain of off-line simulations to the one of DMIs. With this paper, we present a novel approach to real-time physical modelling synthesis, which implements a 2D FDTD solver as a shader program running on the GPU directly within the graphics pipeline. The result is a system capable of running fully interactive, massively sized simulation domains, suitable for novel DMI design. With the help of diagrams and code snippets, we provide the implementation details of a first interactive application, a drum head simulator whose source code is available online. Finally, we evaluate the proposed system, showing how this new approach can work as a valuable alternative to classic GPGPU modelling.