A test with nodal source term

The purpose of this benchmark is to test the source term type of NodalSourceTerm being applied to the hydraulic equation in the computations with the Taylor-Hood elements, e.g., the pressure interpolation using linear shape function, and the displacement interpolation using quadratic shape function.

The problem is solved on a rectangular domain 2 m $\times$ 1 m. Nodal fluid flux is applied on the left boundary nodes with a value of 0.001 kg/s via the property of NodalSourceTerm. The pore pressure on the right boundary is equal to the initial pore pressure of $10^5$ Pa. The displacement in the normal direction of all boundaries except the left one is fixed.

Fluid and solid are incompressible.

All involved parameters are listed in the following tables:

Material Properties
Property Value Unit
Fluid density $10^3$ kg/m$^3$
Viscosity $10^{-3}$ Pa$\cdot$s
Permeability $10^{-14}$ m$^2$
Young’s modulus (bulk) $2.5\cdot 10^9$ Pa
Poisson ratio (bulk) $0.27$ -
Biot coefficient $0.9$ -

The time period of 86400 is discretised into 100 steps.

The distributions of pressure and displacement at the end time are shown in the following figure:

This article was written by Wenqing Wang. If you are missing something or you find an error please let us know.
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