Two-polarisation finite difference model of bowed strings with nonlinear contact and friction forces
Charlotte Desvages, Stefan Bilbao · 2015
Recent bowed string sound synthesis has relied on physical modelling techniques; the achievable realism and flexibility of gestural control are appealing, and the heavier computational cost becomes less significant as technology improves. A bowed string is simulated in two polarisations by discretising the partial differential equations governing its behaviour, using the finite difference method; a globally energy balanced scheme is used, as a guarantee of numerical stability under highly nonlinear conditions. In one polarisation, a nonlinear contact model is used for the normal forces exerted by the dynamic bow hair, left handfingers, andfingerboard. In the other polarisation, a force-velocity friction curve is used for the resulting tangential forces. The scheme update requires the solutionoftwononlinearvectorequations.Soundexamplesandvideo demonstrations are presented.