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Groundwater, which accounts for 30% of freshwater reserves globally, is a vital source for human water supply. Climate change is expected to impact the quality and quantity of groundwater in the future. Numerous studies have shown a positive soil moisture-rainfall feedback through observational data, as well as, numerical simulations. Despite the obvious need to accurately represent soil moisture dynamics, the version-0 of the ACME Land Model (ALM) employs a non-unified treatment of hydrologic processes in the subsurface. Presently, ALM simulates transport of water in the subsurface via a theta-based Richards equation that is loosely coupled to an unconfined aquifer model to account of groundwater–soil water interaction. This ad hoc treatment of vadose–phreatic zone interaction at times results in unphysical model prediction of unsaturated soil layers below predicted water table.
A variably saturated flow model (VSFM) will overcome above-mentioned shortcoming by using pressure-based Richards equation that is valid in unsaturated and saturated zone. The VSFM solver will use finite volume spatial discretization and backward Euler time integration. The nonlinear equations resulting from spatial and temporal discretization will be solved using the Portable, Extensible Toolkit for Scientific Computation (PETSc).
Requirements
Requirement: name-of-requirement-here
Date last modified: 08/31/2015
Contributors: (add your name to this list if it does not appear)
The requirements for VSFM model include:
- Unified treatment of hydrologic processes in the unsaturated and saturated zone.
- An extensible model implementation to enable easy implementation of tightly coupling with other physics formulation (e.g. root hydraulics for ACME v2, thermal processes, etc.)
Algorithmic Formulations
Design solution: short-description-of-proposed-solution-here
Date last modified: 08/20/2015
Contributors: Gautam Bisht
For each requirement, there is a design solution that is intended to meet that requirement. Design solutions can include detailed technical discussions of PDEs, algorithms, solvers and similar, as well as technical discussion of performance issues. In general, this section should steer away from a detailed discussion of low-level software issues such as variable declarations, interfaces and sequencing.
- The governing PDE for flow in porous media is given as:
d/dt (rho * phi * sat) = - Div (rho * q) + Q ... (1)
where
rho = density of water, which is a function of pressure and temperature,
phi = porosity,
sat = liquid saturation
q = darcy flux
Q = source/sink of water (e.g. infiltration, evapotranspiration, bare soil evaporation)
Div = divergence operator
- The Darcy flux is given by q = - k kr / mu * Del (P) ... (2)
where
k = permeability,
kr = relative permeability.
mu = viscosity,
P = liquid pressure
- Following discretization schemes are used to numerically solve Eq (2):
- Spatial discretization: Finite volume,
- Temporal discretization: Backward Euler scheme
- The discretized equations form a system of nonlinear equations.
- Additional details are provided in the attached file (bisht_vsfm_numerical_details_2015_08_31)
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Design and Implementation
Implementation: short-desciption-of-implementation-here
Date last modified: 10/20/2015
Contributors: Gautam Bisht
- Initial prototype of the VSFM model will be developed in MATLAB.
- The VSFM implementation in ACME would use PETSc.
- SNES solver of PETSc will be used to solve the system of nonlinear equations that is obtained after applying spatial and temporal discretization
- The future goal of ACME is to solve tightly coupled transport of water in the soil with other relevant physics (e.g. transport of water in roots [ACME V2]). Thus, the current VSFM will use DMComposite feature of PETSc. DMComposite allows an application to brea
Planned Verification and Unit Testing
Verification and Unit Testing: short-desciption-of-testing-here
Date last modified: 08/20/2015
Contributors: Gautam Bisht
- Unit testing will be added for certain VSFM subroutines (e.g. computation of density, saturation function)
Planned Validation Testing
Validation Testing: short-desciption-of-testing-here
Date last modified: 08/20/2015
Contributors: Gautam Bisht
- The VSFM will be tested against previously benchmark problems published.
- Additionally, VSFM will be tested against PFLOTRAN for certain benchmark problems.
Planned Performance Testing
Performance Testing: short-desciption-of-testing-here
Date last modified: 08/27/2015
Contributors: Gautam Bisht
- Default logging capability of PETSc will be used to examine the performance of VSFM solver (e.g. number of newton steps for the entire simulation, number of linear solves within newton solve, time spent in residual/jacobian evaluation, etc.).
- Additionally, the ACME timing logs with be implemented in the VSFM solver to obtain performance metrics outside the scope of PETSc solver (e.g. time spent in pre and post PETSc solve operations).
- Computational performance will be evaluated for offline and coupled global simulations.