Initial State

At initial condition the pressure is computed using modified Arnold-Brezzi finite elements. This a nonconforming Courzeix-Raviart element modified with an additional quadratic bubble which ensures local conservation of mass in each tetrahedron. The local space contains the full linear polynomial space and as consequence it provides second order accuracy. In contrast finite volume methods use piecewise constant pressure in each cell and are only first order accurate.

At initial condition the principal stresses are derived directly from the FEM approximation of the displacements and the material properties. They are piecewise linear in each element which is the way the Young modulus and Poisson ratio are interpolated on the computational grid. However, due to the underlying discontinuity of the strains, they are discontinuous across element boundaries. >

Minimal Principal Stress

Intermediate Principal Stress

Maximal Principal Stress

At initial condition the total stress tensor components are postprocessed in order to gain one order of accuracy. This is done by first constructing the piecewise constant stresses in each element. The stress components are then interpolated in each vertex utilizing stereoscopic angle weights. This results in a piecewise linear, continuous stress field. These postprocessed stress components can be utilized to compute more accurate principal stresses which are continuous across element boundaries.

Total Stress[1,1]

Total Stress[1,2]

Total Stress[1,3]

Total Stress[2,2]

Total Stress[2,3]

Total Stress[3,3]

At initial condition the saturations are resolved using an explicit first order FV method. They are piecewise constant in each cell. A MAPR linear reconstruction may be uploaded at a later stage.

Initial water saturation

Initial oil saturation