Method of modelling a sedimentary basin using a hex-dominant mesh representation

A computer-implemented method of modelling a sedimentary basin, the sedimentary basin having undergone a plurality of geological events defining a sequence of states of the basin, by means of a computer-executed numerical basin simulation, the numerical basin simulation solving at least one balance equation of poromechanics according to a face-based smoothed finite-element method for determining at least a stress field and a strain field, characterized in that the method comprises carrying out at least the following steps:

• A. performing physical quantity measurements relative to the basin by means of sensors and constructing a mesh representative of the basin for each of the states of the basin, the meshes representative of the basin for each of the states predominantly consisting of hexahedral cells,
• B. by means of the numerical basin simulation and of the meshes for each of the states, determining at least a strain field and a stress field for each of the states by carrying out at least the following steps for each of the meshes representative of the states:
• a) subdividing each of the hexahedral cells of the mesh into at least eight hexahedral subcells,
• b) for each face of each of the subcells, determining a smoothing domain according to the face-based smoothed finite-element method applied to the subcells,
• c) for each of the smoothing domains, determining a strain-displacement relation according to the face-based smoothed finite-element method applied to the smoothing domains,
• d) for each of the smoothing domains, determining a transition relation between the degrees of freedom of the nodes of the subcells containing the smoothing domain and the degrees of freedom of the nodes of the at least one cell to which the subcells belong,
• e) determining a stiffness and nodal forces for each of the smoothing domains from at least the transition relation determined for the smoothing domain and from the strain-displacement relation determined for the smoothing domain,
• f) determining a stiffness and nodal forces relative to the mesh from at least the stiffness and the nodal forces determined for each of the smoothing domains,
• g) modelling the sedimentary basin by determining at least the displacement field and the stress field for the mesh, by means of the numerical basin simulation and at least the stiffness and the nodal forces determined for the mesh.