14th World Congress in Computational Mechanics (WCCM) ECCOMAS Congress 2020 Virtual Congress: 11 – 15 January 2021 F. Chinesta, R. Abgrall, O. Allix and M. Kaliske (Eds) GEOMECHANICAL MODELING USING VARIABLE ORDER SPECTRAL ELEMENT METHOD AT NON-CONFORMAL MESHES ANATOLY VERSHININ¹*, DMITRY KONOVALOV 2 , ALEXEY KUKUSHKIN 3 AND VLADIMIR LEVIN 4 1 Associate professor, Lomonosov Moscow State University, Leninskiye Gory 1, Moscow, Russia, 119991, research scientist at IPE RAS, versh1984@mail.ru https://www.researchgate.net/profile/Anatoly_Vershinin2 2 Team leader, Fidesys LLC, Skolkovo Technopark, Russia, Moscow, office 2.212, building 1, 42 Bolshoy Boulevard, research scientist at IPE RAS, konovalov@cae-fidesys.com, https://www.cae- fidesys.com 3 Team leader, Fidesys LLC, Skolkovo Technopark, Russia, Moscow, office 2.212, building 1, 42 Bolshoy Boulevard, kukushkin@cae-fidesys.com, https://www.researchgate.net/profile/Aleksej_Kukuskin 4 Full professor, Lomonosov Moscow State University, Leninskiye Gory 1, Moscow, Russia, 119991, v.a.levin@mail.ru https://www.researchgate.net/profile/Vladimir_Levin3 Key words: Geomechanics, Spectral element method, Non-conformal discretization, Unstructured mesh, Finite strains, Contact problems, CAE Fidesys. Abstract: The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development of reservoirs and well boring process. The mathematical formulation is based on the theory of repeated superposition of large deformations. A numerical discretization of the posed boundary problems of interacting solids is performed using a discontinuous spectral element method and multi-point constraints at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which