### Parallel Finite Element Model For Coupled Surface And Subsurface Flow In Hydrology: Province Of Santa Fe Basin, Absorbent

#### Abstract

The large spread in length scales present in the hydrological problems (i.e.

province of Santa Fe basin systems) requires a high degree of renement in the nite

element mesh and, then, requires very large computational resources. Also, in a 2D multiaquifer

model, the number of unknowns per surface node is, at least, equal to the number

of aquifers and aquitards. Moreover, if a pollutant transport model is used with the velocity

eld results, then it is desirable to have several sub-layers inside the aquifer in order

to recover the vertical gradient, which drives the transport of pollutant between aquifers.

This increases the number of unknowns and, also, the band-width of the associated FEM

matrix, so that the total computation time is roughly proportional to the square of the

number of vertical layers and sub-layers. Due to this fact, it is expected to have a very

high demand of CPU computation time, calling for parallel processing techniques.

A large scale C++ parallel FEM module using a general advection-diusion PETSc-FEM

code was written for hydrological problems. Several systems of aquifers/aquitards coupled

with a net of surface streams can be solved. The streams can be modelled with the

KWM (Kinematic Wave Model) approximation, 2D or 1D Saint-Venant model. There is

mass exchange between streams and aquifers through a resistance coecient at the stream

walls. Both Manning and Chezy friction models are available for the streams. Absorbent

boundary conditions are implemented in order to avoid wave re

ection for Saint-Venant

models.

province of Santa Fe basin systems) requires a high degree of renement in the nite

element mesh and, then, requires very large computational resources. Also, in a 2D multiaquifer

model, the number of unknowns per surface node is, at least, equal to the number

of aquifers and aquitards. Moreover, if a pollutant transport model is used with the velocity

eld results, then it is desirable to have several sub-layers inside the aquifer in order

to recover the vertical gradient, which drives the transport of pollutant between aquifers.

This increases the number of unknowns and, also, the band-width of the associated FEM

matrix, so that the total computation time is roughly proportional to the square of the

number of vertical layers and sub-layers. Due to this fact, it is expected to have a very

high demand of CPU computation time, calling for parallel processing techniques.

A large scale C++ parallel FEM module using a general advection-diusion PETSc-FEM

code was written for hydrological problems. Several systems of aquifers/aquitards coupled

with a net of surface streams can be solved. The streams can be modelled with the

KWM (Kinematic Wave Model) approximation, 2D or 1D Saint-Venant model. There is

mass exchange between streams and aquifers through a resistance coecient at the stream

walls. Both Manning and Chezy friction models are available for the streams. Absorbent

boundary conditions are implemented in order to avoid wave re

ection for Saint-Venant

models.

#### Full Text:

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**