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The Protoplanetary Discussions conference --- held in Edinburgh, UK, from 7th --11th March 2016 --- included several open sessions led by participants. This paper reports on the discussions collectively concerned with the multiphysics modelling of protoplanetary discs, including the self-consistent calculation of gas and dust dynamics, radiative transfer and chemistry. After a short introduction to each of these disciplines in isolation, we identify a series of burning questions and grand challenges associated with their continuing development and integration. We then discuss potential pathways towards solving these challenges, grouped by strategical, technical and collaborative developments. This paper is not intended to be a review, but rather to motivate and direct future research and collaboration across typically distinct fields based on textit{community driven input}, to encourage further progress in our understanding of circumstellar and protoplanetary discs.
Circumstellar discs may become warped or broken into distinct planes if there is a stellar or planetary companion with an orbit that is misaligned with respect to the disc. There is mounting observational evidence for protoplanetary discs with misali
The dispersal phase of planet-forming disks via winds driven by irradiation from the central star and/or magnetic fields in the disk itself is likely to play an important role in the formation and evolution of planetary systems. Current theoretical m
Damping of the previously discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is studied using the local approach to dynamics of gas-dust perturbations in the limit of the small dust fraction. Turbulence in a disc is r
Dark rings with bright rims are the indirect signposts of planets embedded in protoplanetary discs. In a recent first, an azimuthally elongated AU-scale blob, possibly a planet, was resolved with ALMA in TW Hya. The blob is at the edge of a cliff-lik
Until now, axisymmetric, alpha-disc models have been adopted for calculations of the chemical composition of protoplanetary discs. While this approach is reasonable for many discs, it is not appropriate when self-gravity is important. In this case, s