Omar Duran

A computational mechanician with a solid foundation in reservoir engineering, continuum mechanics, applied mathematics, and finite element methods.

Current Position: Research Scientist, Department of Energy Science and Engineering, Stanford University

Email: oduran@stanford.edu

Education

Postdoctoral fellow in Applied mathematics, CERMICS (ENPC) and INRIA-Paris - Advisor: Alexandre Ern, 11.2019-12.2020

PhD in Science and Petroleum Engineering, Universidade Estadual de Campinas - Advisor: Philippe Devloo, 09.2017

M.Sc. in Science and Petroleum Engineering, Universidade Estadual de Campinas, 02.2013

B.Sc. in Science and Petroleum Engineering, Universidad Industrial de Santander, 11.2010

Research Interests
Projects
Publications
Talks
Student Advisees

Research Interests

I specialize in computational mechanics, emphasizing the development of numerical schemes for solving partial differential equations (PDEs), particularly utilizing finite element techniques. My expertise includes multiphase and compositional flow, geomechanics, reservoir simulation, and computational plasticity.

My research interests are closely tied to the mathematical foundations of numerical methods, particularly finite element methods and their connections to other approximation techniques. I am actively engaged in the study of mixed-dimensional partial differential equations (PDEs) and high-order approximations in both time and space. Additionally, I investigate formulations for compositional multiphase problems, with a specific emphasis on variables related to flash specifications, including the overall composition formulation. Furthermore, I am interested in devising schemes for non-classical continuum mechanics (Cauchy media), including Cosserat elasticity and micropolar media.

Projects

I developed a finite element library for multiphysics applications, utilizing automatic differentiation and a collection of finite elements supported by basix. This library is particularly valuable for prototyping finite element methods for multiphysics problems and extensively explores the concept of graphs and their connections with differential complexes. For more information, please refer to the repository: nfempy.

Publications

ORCID Google Scholar ResearchGate

Current

  • Veljko Lipovac: Ph.D. in Applied Mathematics, University of Bergen, Bergen, Norway (08.2021 – Present). Co-advised with Prof. Inga Berre.

Past

  • Sundus Iqbal: M.Sc. in Applied Mathematics, University of Bergen, Bergen, Norway (10.2023 – 12.2024). Co-advised with Prof. Kundan Kumar.
  • Jose Villegas: Ph.D. in Science and Petroleum Engineering, Universidade Estadual de Campinas, São Paulo, Brazil (03.2018 – 07.2023). Co-advised by Prof. Philippe Devloo.
  • Ingrid Kristine Jacobsen: M.Sc. in Applied Mathematics, University of Bergen, Bergen, Norway (01.2022 – 06.2022).
  • Solveig H. Stefansdottir: M.Sc. in Applied Mathematics, University of Bergen, Bergen, Norway (01.2023 – 07.2023). Co-advised with Prof. Kundan Kumar.

Contact Information

Feel free to get in touch via email or through my GitHub profile.