add a cookbook that reproduces the van Keken 2008 corner flow subduct…

…ion benchmark

cookbooks/vankeken_subduction/doc/vankeken_subduction.md

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+# Van Keken 2008 corner flow recreation
+
+*This section was contributed by Daniel Douglas, Cedric Thieulot, Wolfgang Bangerth, and Max Rudolph*.
+
+This cookbook recreates a 2D corner flow style subduction model as outlined in {cite:t}`vankeken:etal:2008`. Since ASPECT uses a rectangular mesh by default, prescribed internal velocities along a dipping (slab) produces unstable Stokes solver convergence behavior and an unstable pressure solution. To circumvent this issue, a custom mesh with a $Q_2\times Q_1$ discretization was designed that allows cell edges to align with the internal boundaries defining where internal velocities within the subducting plate are assigned. Further efforts to confirm that this setup can accurately reproduce the results of the 2008 benchmark should be done to move this from the cookbook section to the benchmark section.
+
+The model prescribes a 5cm/yr convergence rate at a subduction angle of 45 degrees along the left boundary and the interface between the subducting plate, the overriding plate, and mantle wedge. In the overriding plate, the velocity is constrained to be 0. The Stokes equations are solved in the mantle wedge, and the right and bottom boundaries are open to ensure mass conservation.
+
+The half space cooling model prescribed on the left boundary is advected downdip at the prescribed convergence rate, creating the slab. The cold slab interacts with the mantle wedge, resulting in a classic corner flow temperature (figure 1) and velocity field (figure 2). The geometry of the model requires a very low dynamic pressure in the corner of the mantle wedge, and with the specialized mesh the pressure field was able to be solved for using a continuous $Q_1$ discretization, as shown in figure 2. The model proceeds until a steady state thermal structure is reached for the entire model domain.
+
+```{figure-md} fig:vanKeken-temperature
+<img src="velocity_field.png" alt="Screenshot"  width="100%"/>
+The temperature field of the subducting slab after ~100 Myr. A half space cooling model is applied to the left boundary, which is advected at a 45 degree angle at a rate of 5 cm/yr within the subducting plate.
+```
+
+```{figure-md} fig:vanKeken-velocity
+<img src="velocity_field.png" alt="Screenshot"  width="100%"/>
+The velocity field of the subducting slab after ~100 Myr which is advected at a 45 degree angle at a rate of 5 cm/yr within the subducting plate.
+```
+
+```{figure-md} fig:vanKeken-pressure
+<img src="pressure_mesh.png" alt="Screenshot"  width="100%"/>
+The pressure field in the corner of the mantle wedge. The pressure solution was solved using a continuous $Q_1$ discretization, which was made possible with the custom mesh design used for this cookbook.
+```

cookbooks/vankeken_subduction/plugin/CMakeLists.txt

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+CMAKE_MINIMUM_REQUIRED(VERSION 2.8.12)
+
+FIND_PACKAGE(Aspect REQUIRED HINTS ${Aspect_DIR} ../ ../../ $ENV{ASPECT_DIR})
+DEAL_II_INITIALIZE_CACHED_VARIABLES()
+
+SET(TARGET "vankeken_subduction")
+PROJECT(${TARGET})
+
+ADD_LIBRARY(${TARGET} SHARED van_Keken_mesh.cc ../../prescribed_velocity/prescribed_velocity.cc)
+ASPECT_SETUP_PLUGIN(${TARGET})