Daniele Moretto

Daniele Moretto, Andrea Franceschini, Massimiliano Ferronato

The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational grids for such problems often remains one of the main bottlenecks. The use of a domain partitioning with non-conforming grids is a possible solution, which, however, requires the development of robust and efficient inter-grid interpolation operators to transfer a scalar or a vector field from one domain to another. This work presents a novel approach for interpolating quantities across non-conforming meshes within the framework of the classical mortar method, where weak continuity conditions are enforced. The key contribution is the introduction of a novel strategy that uses mesh-free Radial Basis Function (RBF) interpolations to compute the mortar integral, offering a compelling alternative to traditional projection-based methods. We propose an efficient algorithm tailored for complex three-dimensional settings allowing for potentially significant savings in the overall computational cost and ease of implementation, with no detrimental effects on the numerical accuracy. The formulation, analysis, and validation of the proposed RBF-based algorithm is discussed with the aid of a set of numerical examples, demonstrating its effectiveness. Furthermore, the details of the implementation are discussed and a test case involving a complex geometry is presented, to illustrate the applicability and advantages of our approach in real-world problems.

Daniele Moretto, Andrea Franceschini, Massimiliano Ferronato

Accurate numerical simulation of fault and fracture mechanics is critical for the performance and safety assessment of many subsurface systems. The discretized representation of discontinuity surfaces and the robust simulation of their frictional contact behavior still represent major challenges. In this work, we use the mortar method to enforce the contact constraints and allow for non-conformity around the discontinuity surface, with a set of Lagrange multipliers playing the role of interface tractions. The formulation combines piecewise linear displacements with piecewise constant multipliers defined on one side of the fault interface (the non-mortar side). This choice for the Lagrange multipliers has a number of advantages from practical and computational viewpoints, but violates the inf-sup stability constraint. In order to stabilize the proposed formulation, we develop a traction-jump stabilization term to be added to the constraint equations. We use a macro-element analysis to derive an algorithmic strategy that automatically evaluates the proper scaling of the stabilization, without requiring any additional user-selected parameter. Numerical experiments demonstrate that the proposed formulation not only restores the inf-sup stability condition, but also recovers stable traction profiles in the presence of finer non-mortar sides, where other inf-sup-stable formulations fail. The proposed method is finally used to simulate non-linear contact conditions in non-conforming corner-point grids typically used in industrial geological applications.