About

Yuri Bazilevs is the E. Paul Sorensen Professor of Engineering and serves as the Program Director at Brown University. His research focuses on computational engineering, specifically within the context of data-enabled computational engineering and science. He is affiliated with the School of Engineering at Brown University, located in Providence, RI. As a faculty member, he contributes to advancing the field through both research and leadership in engineering education.

Research topics

• Computer Science
• Mathematics
• Engineering
• Mathematical analysis
• Structural engineering
• Geometry
• Artificial Intelligence
• Physics
• Mechanics
• Algorithm
• Applied mathematics
• Mathematical optimization

Selected publications

• Weak wall boundary conditions for compressible flows

  Engineering With Computers · 2026-01-14 · 1 citations

  articleOpen accessSenior author

  Weak imposition of essential boundary conditions (i.e., weak BCs) for the Navier-Stokes equations of incompressible flows allows a certain amount of controlled numerical flow slip on the solid surface. Numerical flow slip mimics the presence of a thin boundary layer that would otherwise need to be captured using a fine mesh resolution. As a result, weak BCs enable the use of coarser meshes near solid walls without sacrificing numerical solution accuracy, which significantly reduces the computational costs, especially for 3D, wall-bounded turbulent flows. However, weak BCs for compressible flows are not as well understood as those for the incompressible-flow case. In particular, numerical instabilities were observed in some cases where the weak BCs were simultaneously imposed for the velocity and temperature fields. In the present effort, to address these stability issues, we develop a methodology for the design of compressible-flow weak BC operators and demonstrate the improved performance of the resulting weak BC formulations using challenging 2D and 3D test cases.

  PublisherOA PDFDOI

• A naturally sharpened level-set formulation for incompressible free-surface flows

  Computer Methods in Applied Mechanics and Engineering · 2026-02-13

  articleOpen accessSenior authorCorresponding

  The level set method is widely employed in two-phase flow simulations due to its robustness in handling complex interface topological changes. However, it suffers from two main limitations. First, the method is not inherently mass conservative. Second, the signed-distance property of the level set field can deteriorate under strong convection, particularly in high Reynolds-number flows. Consequently, conventional level set methods often require auxiliary procedures such as sharpening (or re-distancing) and mass correction, which rely on and are sensitive to user-defined parameters and also increase implementation complexity and computational cost. Here, we present a naturally sharpened level-set formulation for incompressible air-water flows that is mass conservative and eliminates the need for these additional algorithmic steps. The resulting free-surface flow modeling and simulation framework is more efficient and robust as demonstrated through several challenging numerical test cases.

  PublisherDOI

• Proximal Galerkin for Phase Field Fracture

  ArXiv.org · 2026-04-29

  articleOpen accessSenior author

  The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and boundedness of the phase-field variable. This work proposes the proximal Galerkin (PG) methodology as a robust and efficient framework for solving phase-field fracture problems. By reformulating the inequality-constrained optimization problem into a sequence of saddle-point problems involving latent variables, the PG method rigorously enforces the physical bounds of the phase-field variable and naturally handles the irreversibility condition. This approach is directly applicable to both static and dynamic phase-field fracture problems. The numerical results demonstrate that the PG framework accurately reproduces theoretical predictions and experimental observations, while offering a unified, mathematically consistent treatment of the constraints inherent to phase-field fracture modeling.

  PublisherOA PDF

• Proximal Galerkin for Phase Field Fracture

  arXiv (Cornell University) · 2026-04-29

  preprintOpen accessSenior author

  The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and boundedness of the phase-field variable. This work proposes the proximal Galerkin (PG) methodology as a robust and efficient framework for solving phase-field fracture problems. By reformulating the inequality-constrained optimization problem into a sequence of saddle-point problems involving latent variables, the PG method rigorously enforces the physical bounds of the phase-field variable and naturally handles the irreversibility condition. This approach is directly applicable to both static and dynamic phase-field fracture problems. The numerical results demonstrate that the PG framework accurately reproduces theoretical predictions and experimental observations, while offering a unified, mathematically consistent treatment of the constraints inherent to phase-field fracture modeling.

  PublisherDOI

• Polymer-based architected materials and structures: Geometry, experiments, constitutive modeling, and advanced simulations

  International Journal of Solids and Structures · 2026-02-17

  articleOpen accessSenior author
  PublisherDOI

• An efficient NURBS-based reconstruction approach to isogeometric analysis of triply periodic minimal surface structures

  Engineering With Computers · 2025-09-23 · 2 citations

  article
  PublisherDOI

• An efficient naturally sharpened stabilized multiphase flow formulation for modeling underwater explosions

  Computational Mechanics · 2025-06-18 · 3 citations

  articleSenior author
  PublisherDOI

• Generalizing CAS elements to overcome locking in $$C^1$$-continuous cubic NURBS-based discretizations

  Engineering With Computers · 2025-02-07

  article
  PublisherDOI

• Isogeometric analysis of underwater explosion fluid–structure interaction (UNDEX-FSI)

  Computational Mechanics · 2025-02-10 · 7 citations

  articleSenior author
  PublisherDOI

• Polymer-Based Architected Materials and Structures: Geometry, Experiments, Constitutive Modeling, and Advanced Simulations

  SSRN Electronic Journal · 2025-01-01

  preprintOpen accessSenior author
  PublisherDOI

Recent grants

• Collaborative Research: LES and RANS simulations of estuarine flows: Understanding and parameterizing the role of Langmuir turbulence

  NSF · $178k · 2018–2021

• CAREER: Fluid-Structure Interaction and High-Performance Computing for Wind Energy Applications

  NSF · $459k · 2011–2017

Frequent coauthors

• Ming‐Chen Hsu

  89 shared

• Tayfun E. Tezduyar

  Rice University

  75 shared

• Kenji Takizawa

  Waseda University

  64 shared

• Artem Korobenko

  University of Calgary

  60 shared

• Thomas J.R. Hughes

  58 shared

• Masoud Behzadinasab

  Brown University

  56 shared

• David Kamensky

  42 shared

• Yongjie Zhang

  Guangdong Medical College

  36 shared