**Solver Fortran File:**`Flowdepth.f90`

**Solver Name:**`FlowdepthSolver`

**Required Output Variable(s):**`Depth`

or`Height`

(user defined)**Required Input Variable(s):**None**Optional Output Variable(s):**`FreeSurf`

,`FreeSurfGrad1`

,`FreeSurfGrad2`

(`FreeSurf`

name is user defined)**Optional Input Variable(s):**None

This solver computes the vertical distance from a surface (either free surface or bedrock in Glaciology). In structured FD-grids this is a trivial procedure - not so in unstructured FEM meshes as used by Elmer. A degenerated Poisson equation has to be solved in order to get nodal values for either the flow depth below the free surface or the flow height above the bedrock. It can also compute the horizontal derivative of the upper/lower surface if `Depth`

/`height`

is calculated.

Alternatively, if you are using a structured mesh, you might consider replacing the `FlowDepth solver`

by the `StructuredProjectToPlane solver`

, as explained here.

The required keywords in the SIF file for this solver are:

! This solves the depth underneath the free surface !-------------------------------------------------- Solver 1 Equation = "Flowdepth" Exec Solver = "Before Timestep" Procedure = File "ElmerIceSolvers" "FlowDepthSolver" Variable = String "Depth" Variable DOFs = 1 Linear System Solver = "Direct" Linear System Direct Method = "UMFPACK" ! this sets the direction ! -1 is negative z-direction (upside down) ! +1 is positive (downside up) Gradient = Real -1.0E00 ! switch that to True, if you want to have ! free surface gradients to be computed !------------------------------------ Calc Free Surface = Logical True ! the name for the exported (if not existing) added variable ! the gradients will be stored in variables with the base ! name given and "Grad1" and (in 3 dimensions) "Grad2" added, ! so in our case "FreeSurfGrad1" and "FreeSurfGrad2" ! again, if those variables did not exist, they will be ! automatically created !----------------------------------------------------------- Freesurf Name = String "FreeSurf" End ! This solves the height above the bedrock !------------------------------------------ Solver 2 Equation = "Flowheight" ! mind different name Exec Solver = "Before Timestep" Procedure = File "Flowdepth2" "FlowDepthSolver" ! make a copy of the original solver, to get a separate address space Variable = String "Height" ! mind different name for variable Variable DOFs = 1 Linear System Solver = "Direct" Linear System Direct Method = "UMFPACK" Gradient = Real 1.0E00 ! this time positive Calc Free Surface = Logical False End ! boundary at the free surface !----------------------------- Boundary Condition 1 ... Depth = Real 0.0 End ! boundary at bedrock !----------------------------- Boundary Condition 2 ... Height = Real 0.0 End ! internal boundary with ! no Dirichlet and neither ! the default Neumann condition !----------------------------- Boundary Condition 3 ... Flowdepth Skip = Logical True End

Tests using the `FlowDepth`

and `FlowHeight`

solvers can be found in `[ELMER_TRUNK]/elmerice/Tests/FlowDepth`

and `[ELMER_TRUNK]/elmerice/Tests/FlowHeight `

.