Table 2 Boundary conditions imposed in the subduction zone model domain

Velocity

Free slip

\(\varvec{u} \cdot \hat{\varvec{n}} = 0\)

and \((\varvec{\sigma }\cdot \hat{\varvec{n}}) \cdot \hat{\varvec{\tau }}_i = \varvec{0}\),

\(i=1,\ldots ,D-1\)

\({\partial \Omega _\text {top} \cup \partial \Omega _\text {near} \cup \partial \Omega _\text {far} \cup \partial \Omega _\text {bottom}}\)

Natural in/outlet

\(\varvec{\sigma }\cdot \hat{\varvec{n}} = \varvec{0}\)

\(\partial \Omega _\text {slab inlet} \cup \partial \Omega _\text {slab outlet} \cup \partial \Omega _\text {wedge outlet}\)

Velocity coupled

driven slab

\(\varvec{u} = u_\text {conv} \hat{\varvec{\tau }}_\text {conv} + \varvec{u}_\text {slab}\)

\(\Gamma _\text {slab} \cup \Gamma _\text {slab fault}\)

Fault zone no slip

\(\varvec{u} = \varvec{u}_\text {slab}\)

\(\Gamma _\text {wedge no slip}\)

Temperature

Surface temperature

\(T = T_0\)

\(\partial \Omega _\text {top}\)

Inlet slab temperature

\(T = T_\text {in}\)

\(\partial \Omega _\text {slab inlet}\)

Outlet temperature

influx

\(T = T_\text {out}\)

\(\partial \Omega _\text {wedge outlet} \cup \partial \Omega _\text {slab outlet}\)

where \(\varvec{u} \cdot \hat{\varvec{n}} < 0\)

Outlet temperature

outflux

\(k \nabla T \cdot \hat{\varvec{n}} = 0\)

\(\partial \Omega _\text {wedge outlet} \cup \partial \Omega _\text {slab outlet}\)

where \(\varvec{u} \cdot \hat{\varvec{n}} \ge 0\)

Zero heat flux

\(k \nabla T \cdot \hat{\varvec{n}} = 0\)

\(\partial \Omega _\text {near} \cup \partial \Omega _\text {far} \cup \partial \Omega _\text {bottom}\)

Temperature coupling

\(T_\text {slab} \hat{\varvec{n}}_\text {slab} = - T_\text {plate} \hat{\varvec{n}}_\text {plate}\)

and \(T_\text {slab} \hat{\varvec{n}}_\text {slab} = - T_\text {wedge} \hat{\varvec{n}}_\text {wedge}\)

\(\Gamma _\text {slab} \cup \Gamma _\text {wedge no slip} \cup \Gamma _\text {slab fault}\)