Neumann BC superposed with a Dirichlet Seepage BC
Miguel Calpe
Dear all,
We have a topography
divided into two parts: (i) sea for cells with z<0m and (ii) land for cells
with z> 0m. At the sea, a hydrostatic BC is applied. At the land part, we superpose
two BC: (1) Neumann flux, and (2) a Dirichlet Seepage BC. Please see the
schematic representation below and the attached input file.
By
superposing the Neumann BC denoted by R with the Dirichlet Seepage BC denoted
by -D, I would like to apply a recharge (R) only on those land cells
where the water table is below the topography level and a discharge (-D)
applied on those cells where the water table is above the topography level until
the water table equals the topography level.
Could you please confirm that by superposing these two BC we obtain the desired mixed BC?
Thank you for the help
Best regards,
Miguel
Hammond, Glenn E
Miguel,
Differentiating between boundary cell faces above and below the water table is currently not possible. However, we frequently superimpose Neumann and (Dirichlet) Seepage boundary conditions to accommodate what you describe below. You can assign both boundary conditions to the ENTIRE top of the domain (including the sea portion, if you so desire). For the boundary cells that are saturated (i.e., below the water table or sea level), the Neumann BC will increase the pressure in the cell slightly higher than the hydrostatic pressure and cause the Dirichlet BC to expel the water introduced (injected) by the Neumann BC. Some researchers have been skeptical of this approach in the past, saying it is inaccurate or unrealistic, but the alternative approach is a complicated mixed boundary condition which may deteriorate convergence. I only see issues with the superposition (i.e., inaccurately high pressures in cells) if the permeability is very small.
Glenn
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Sent: Wednesday, November 22, 2023 6:17 AM
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Subject: [pflotran-users: 7390] Neumann BC superposed with a Dirichlet Seepage BC
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Dear all,
We have a topography divided into two parts: (i) sea for cells with z<0m and (ii) land for cells with z> 0m. At the sea, a hydrostatic BC is applied. At the land part, we superpose two BC: (1) Neumann flux, and (2) a Dirichlet Seepage BC. Please see the schematic representation below and the attached input file.
By superposing the Neumann BC denoted by R with the Dirichlet Seepage BC denoted by -D, I would like to apply a recharge (R) only on those land cells where the water table is below the topography level and a discharge (-D) applied on those cells where the water
table is above the topography level until the water table equals the topography level.
Could you please confirm that by superposing these two BC we obtain the desired mixed BC?
Thank you for the help
Best regards,
Miguel
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