<p><strong>Melting at convergent plate boundaries</strong></p><p>At divergent plate boundaries hot mantle upwelling is associated with abundant melt generation and volcanism. At convergent plate boundaries such as subduction zones and continental collision zones thick and cold plates feed mantle downwellings. Yet these "cold" regions also show abundant volcanic activity with mean volcanic output rates of almost similar order of magnitudes (White et al., 2006, G-cubed). Responsible melt generation mechanisms are addressed including a) volatile driven decrease of the solidus temperature, b) decompressional melting in the mantle wedge or in shallow asthenosphere associated with delamination, or c) increased radiogenic heating within thickened continental crust.&#160;&#160;&#160; &#160;</p><p><strong>Melt transport mechanisms</strong></p><p>The above processes form partially molten regions. By which mechanism(s) does the melt segregate out of the melt source region and rise through the mantle or crust. The basic mechanism is two-phase flow, i.e. a liquid phase percolates through a solid, viscously deforming matrix. The corresponding equations and related issues such as compaction or effective matrix rheology are addressed. Beside simple Darcy flow, special solutions of the equations are addressed such as solitary porosity waves. Depending on the bulk to shear viscosity ratio of the matrix and the non-dimensional size of these waves, they show a variety of features: they may transport melt over large distances, or they show transitions from rising porosity waves to diapiric rise or to fingering. Other solutions of the equations lead to channeling, either mechanically or chemically driven. One open question is how do such channels transform into dykes which have the potential of rising through sub-solidus overburden. A recent hypothesis addresses the possibility that rapid melt percolation may reach the thermal non-equilibrium regime, i.e. the local temperature of matrix and melt may evolve differently. &#160;Once dykes have been formed they may propagate upwards driven by melt buoyancy and controlled by the ambient stress field. As another magma ascent mechanism diapirism is addressed. &#160;</p><p><strong>Modelling magmatic systems in thickened continental crust </strong></p><p>Once basaltic melts rise from subducting slabs, they may underplate continental crust and generate silicic melts. Early dynamic models (Bittner and Schmeling, 1995, Geophys. J. Int.) showed that such silicic magma bodies may rise to mid-crustal depth by diapirism. More recent approaches (e.g. Blundy and Annan, 2016, Elements) emplace sill intrusions into the crust at various levels and calculate the thermal and melting effects responsible for the formation of mush zones. Recently Schmeling et al. (2019, Geophys. J. Int.) self-consistently modelled the formation of crustal magmatic systems, mush zones and magma bodies by including two-phase flow, melting/solidification and effective power-law rheology. In these models melt is found to rise to mid-crustal depths by a combination of compaction/decompaction assisted two-phase flow, sometimes including solitary porosity waves, and diapirism. An open question in these models is whether or how dykes may self-consistently form to transport the melts to shallower depth. First models which combine the two-phase flow crustal models with elastic dyke-propagations models (Maccaferri et al., 2019, G-cubed) are promising.&#160;&#160;&#160; &#160;&#160;</p><p>&#160;&#160;&#160; &#160;&#160;</p>
Quantitative modeling of granitic melt generation and segregation in the continental crust
