About

Dr. Christopher Roy is a Professor and the Assistant Department Head for Graduate Studies in the Kevin T. Crofton Department of Aerospace and Ocean Engineering at Virginia Tech. He holds a Ph.D. in Aerospace Engineering from North Carolina State University, an M.S. in Aerospace Engineering from Texas A&M University, and a B.S.E. in Mechanical Engineering and Materials Science from Duke University. His research expertise centers on Computational Fluid Dynamics, with a particular focus on Verification and Validation in scientific computing. Dr. Roy has contributed significantly to the field through his involvement in professional service, including roles such as Associate Fellow of the American Institute of Aeronautics and Astronautics, member of the AIAA Fluid Dynamics Technical Committee, and organizer of key conferences and short courses related to verification and validation. His teaching includes graduate courses in Verification and Validation in Scientific Computing, Computational Fluid Dynamics, and Turbulence Modeling and Simulation, as well as undergraduate courses in Aerodynamics and Hydrodynamics. Recognized for his contributions, Dr. Roy has received numerous awards, including the Presidential Early Career Award for Scientists and Engineers, the Faculty Fellow Award from Virginia Tech's College of Engineering, and several honors from Auburn University and NASA. His professional service and research continue to advance the understanding and application of fluid dynamics in aerospace engineering.

Research topics

• Computer Science
• Aerospace engineering
• Marine engineering
• Simulation
• Engineering
• Physics
• Mechanics
• Mechanical engineering
• Geology
• Systems engineering
• Algorithm
• Structural engineering
• Mathematics

Selected publications

• Application of Machine-Learned Turbulence Models for Improved Predictions in Hypersonic Flows

  2026-01-08

  article

  The current work describes machine learned modifications to the Menter SST-V turbulence model for improved Reynolds-Averaged Navier-Stokes (RANS) model predictions. A neural network learned a physical mapping between the scalar invariants of a RANS simulation flow field and turbulence closure variables based on Pope’s more general effective-viscosity hypothesis. Model training was performed on an axisymmetric large cone-flare geometry at Mach 6.17. The trained Menter SST-V model demonstrated improved predictions in surface pressure and heat transfer for the same large cone-flare at Mach 5.9 and for a Mach 7 ogive cylinder-flare.

  PublisherDOI

• Three-Dimensional Effects of the Flow Over the BeVERLI Hill

  2026-01-08

  article

  Three-dimensional turbulent boundary layers are commonly generated in engineering flows exposed to surface curvature and spatially varying pressure gradients, yet their detailed structure and dynamics remain insufficiently understood. In this study, a canonical three-dimensional turbulent boundary layer developing over a complex hill geometry is examined using high-resolution Laser Doppler Velocimetry (LDV) measurements and complementary steady Reynolds-averaged Navier-Stokes simulations. Measurements were acquired at four streamwise stations in the Virginia Tech Stability Wind Tunnel at a hill-height-based Reynolds number of 250{,}000. The results reveal that while the near-wall region remains approximately collateral up to 60 wall-normal units, strong three-dimensional effects emerge farther from the wall in regions influenced by pressure gradients and curvature. These effects manifest as pronounced flow skewness, the formation of distinct inner and outer layers, and elevated turbulence anisotropy. Stations exposed to mild pressure gradients exhibit comparatively thinner and more two-dimensional boundary layers, whereas strong adverse pressure gradients promote outer-layer thickening and flow separation. The CFD simulations successfully reproduce the primary qualitative trends in mean flow, although quantitative deviations persist near separation. These findings demonstrate the significant sensitivity of turbulent boundary layer structure to three-dimensional pressure-gradient and surface curvature. The combined experimental and computational dataset provides a valuable reference for evaluating turbulence models in complex non-equilibrium flows and offers insight relevant to aerodynamic design applications involving separation-prone geometries.

  PublisherDOI

• The Effect of Discretization Error on Training of Machine-Learned Turbulence Models

  2026-01-08

  article

  A study on the effect of discretization error (DE) on Machine-Learning (ML) turbulence models is conducted. Data Assimilation and Field Inversion is used to learn turbulence models on three different grid resolutions for the simulation of hypersonic flow over a flat plate. Two kinds of training are conducted to learn a mapping between local scalar invariants and turbulent transport quantities. The first training uses a very fine grid as ``truth'' data, and the second uses velocity and temperature boundary layer profiles from a direct numerical simulation of hypersonic flow over a flat plate. It is found that ML turbulence models have enough degrees of freedom to correct for DE, but that physics-based ML turbulence models exhibit nonphysical results for untrained variables when a large amount of DE is present on training grids. It is also found that the relationship between DE during training and model error during testing is not 1:1 and that small amounts of DE during training can have disproportionate impacts on the final turbulence model.

  PublisherDOI

• Verification, Validation, and Uncertainty Quantification in Scientific Computing

  Cambridge University Press eBooks · 2025-03-22 · 5 citations

  bookSenior author

  Can you trust results from modeling and simulation? This text provides a framework for assessing the reliability of and uncertainty included in the results used by decision makers and policy makers in industry and government. The emphasis is on models described by PDEs and their numerical solution. Procedures and results from all aspects of verification and validation are integrated with modern methods in uncertainty quantification and stochastic simulation. Methods for combining numerical approximation errors, uncertainty in model input parameters, and model form uncertainty are presented in order to estimate the uncertain response of a system in the presence of stochastic inputs and lack of knowledge uncertainty. This new edition has been extensively updated, including a fresh look at model accuracy assessment and the responsibilities of management for modeling and simulation activities. Extra homework problems and worked examples have been added to each chapter, suitable for course use or self-study.

  PublisherDOI

• Data-Driven Turbulence Modeling Approach for Cold-Wall Hypersonic Boundary Layers

  Journal of Thermophysics and Heat Transfer · 2025-10-13 · 2 citations

  article

  Wall-cooling effect in hypersonic boundary layers can significantly alter the near-wall turbulence behavior, which is not accurately modeled by traditional Reynolds-averaged Navier–Stokes turbulence models. To address this shortcoming, this paper presents a turbulence modeling approach for hypersonic flows with cold-wall conditions using an iterative ensemble Kalman method. Specifically, a neural-network-based turbulence model is used to provide closure mapping from mean flow quantities to Reynolds stress as well as a variable turbulent Prandtl number. Sparse observation data of velocity and temperature are used to train the turbulence model. This approach is analyzed using a direct numerical simulation database for zero-pressure gradient boundary-layer flows over a flat plate with a Mach number between 6 and 14 and wall-to-recovery temperature ratios ranging from 0.18 to 0.76. Two training cases are conducted: 1) a single training case with observation data from one flow case, and 2) a joint training case where data from two flow cases are simultaneously used for training. Trained models are also tested for generalizability on the remaining flow cases in each of the training cases. The results are also analyzed for insights to inform the future work toward enhancing the generalizability of the learned turbulence model.

  PublisherDOI

• Improved Data Assimilation for Hypersonic Machine-Learned Turbulence Modeling

  2025-07-16

  articleSenior author

  Recently, machine learning methodologies have demonstrated the ability to substantially improve Reynolds-averaged Navier-Stokes (RANS) computational models. The current work applies Data Assimilation and Field Inversion (DAFI) to train a Neural Network (NN) to learn two parameters, g^(1) and Pr_t, for closure of the k-ω SST turbulence model. The NN learns a mapping between scalar invariants in the flowfield and g^(1) and Pr_t fields, which embeds Galilean invariance into the turbulence model. The NN model is trained separately on two different cases to produce two different turbulence models. The first case uses Direct Numerical Simulation (DNS) data for Mach 5.86 flow over a flat plate. The second cases uses experimental data for Mach 7.11 flow over a 20° cylinder flare. The trained NN models were used to predict Mach 11 flow over a cone flare. Both models demonstrated improvement over the baseline k-ω SST model. The model trained on the cylinder flare predicts flow in the recirculation zone of the cone flare much better than either the k-ω SST model or the model trained on the flat plate data.

  PublisherDOI

• Planning, Management, and Implementation Issues

  Cambridge University Press eBooks · 2025-03-22

  book-chapterSenior author

  This final section of the book primarily deals with the topic of how managers – both line managers and project managers – plan, implement, develop, and sustain verification, validation, and uncertainty quantification (VVU however, our experience and the experience of others has convinced us that while technical issues and computing resources are important, they are not the limiting factor in improving the credibility and usefulness of scientific computing used in a decision-making environment. We point out that although computing speed has continued to increase by a factor of ten every four years for multiple decades, we do not believe there has been a comparable impact of the information produced in modeling and simulation (M&S). We believe that nontechnical issues have significantly constrained improvements in the credibility of the information produced in M&S. Examples of these issues are (a) poor allocation of resources relative to the simulation needs of a project, (b) inadequate and ambiguous characterization and understanding of uncertainties in simulations, and (c) the difficulty of management and staff to assess how the time and resources invested in VV&UQ produce a net benefit for the credibility of the simulation results produced.

  PublisherDOI

• Assessment of Turbulence Models for Hypersonic Turbulent Flat Plate Boundary Layers

  2025-01-03 · 1 citations

  article

  Many hypersonic flow applications have “cold” walls, where the wall temperature is considerably lower than the recovery, or adiabatic, wall temperature (Tw/Tr < 1), due to radiative cooling and conduction of heat into the surface. Currently, the most widely used zero-, one-, and two-equation Reynolds-Averaged Navier-Stokes (RANS) and Favre-Averaged Navier-Stokes (FANS) equations turbulence models have inherent weaknesses and require further assessment. This study looks at various hypersonic cold-wall turbulent boundary layer flat plate cases from a recent DNS database. Both the Menter k-ω Shear Stress Transport (SST) turbulence model and Spalart-Allmaras (SA) turbulence model are implemented in an in-house compressible CFD code SENSEI. Simulations are run on coarse, medium, fine, and ultrafine grids with a constant turbulent Prandtl number of PrT = 0.9, and other simulations are run on the fine grids with three different variable turbulent Prandtl number algebraic models. Profiles of the velocity, temperature, turbulent kinetic energy (TKE), Reynolds stresses, wall skin friction coefficient, and wall heat transfer coefficient from the SENSEI CFD code are compared to the DNS data. For the velocity, the Menter k-ω SST model underpredicts the DNS with low Tw/Tr, the SA model underpredicts the DNS with high M and high Tw/Tr, and both models diverge from the DNS in the log and outer regions of the boundary layer. For the temperature, the SA model better matches the DNS than the Menter k-ω SST model, except in the log region. For the TKE, the Menter k-ω SST model underpredicts the DNS in the buffer and log regions, especially the peak of the TKE, but overpredicts the DNS in the outer region. For the Reynolds stresses, the Menter k-ω SST model underpredicts the DNS of the x-direction normal stress, overpredicts the DNS of the y-direction normal stress, better matches the DNS of the z-direction normal stress with high Tw/Tr and low M, and overpredicts the DNS of the xy-direction shear stress with low Tw/Tr and high M. For the skin friction coefficient, the SA model better matches the slope of the DNS, and better matches the DNS with high Tw/Tr. Meanwhile, the Menter k-ω SST model underpredicts the DNS with low Retau. For the wall heat transfer coefficient, the SA model better matches the slope of the DNS, but both models underpredict the DNS with low Retau. The comparison of the three different variable turbulent Prandtl number algebraic models with a constant turbulent Prandtl number show that a well-tailored variable model has the ability to improve predictions with the Menter k-ω SST model, while keeping computational cost and code complexity low. Future work for this study includes further exploration of grid convergence, and of another high M and low Tw/Tr case from the DNS database

  PublisherDOI

• Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations

  Journal of Computational Physics · 2025-02-24 · 3 citations

  article
  PublisherDOI

• Application of Error Transport Equations for Unsteady Problems With Discontinuities

  2025-01-03

  article

  Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics challenging for traditional experimental methods. Despite its widespread use, the accuracy of CFD results remains contingent upon the underlying modeling and numerical errors. A key aspect of ensuring simulation reliability is the accurate quantification of discretization error (DE), which is the difference between the simulation solution and the exact solution to the governing partial differential or integral equations. This study addresses estimating DE through Error Transport Equations (ETE), an additional set of equations closely related to the original equations. Historically, Richardson extrapolation has been a mainstay for DE estimation due to its simplicity and effectiveness. However, the method's feasibility diminishes with increasing computational demands, particularly in large-scale and high-dimensional problems. The integration of ETE into existing CFD frameworks is facilitated by their compatibility with existing numerical codes, minimizing the need for extensive code modification. By incorporating techniques developed for treating discontinuities, this study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on Sod's shock tube problem.

  PublisherDOI

Frequent coauthors

• K. Todd Lowe

  Virginia Tech

  30 shared

• William J. Devenport

  26 shared

• Aldo Gargiulo

  Virginia Tech

  24 shared

• Aurélien Borgoltz

  Virginia Tech

  20 shared

• Julie E. Duetsch-Patel

  Boeing (Australia)

  16 shared

• William L. Oberkampf

  15 shared

• Aniruddha Choudhary

  Indian Institute of Technology Madras

  15 shared

• Tyrone Phillips

  University of British Columbia

  15 shared

Labs

• Christopher Roy LabPI

Awards & honors

• Faculty Fellow Award, College of Engineering, Virginia Tech,…
• Presidential Early Career Award for Scientists and Engineers…
• Associate Fellow, American Institute of Aeronautics and Astr…
• DOE Defense Programs Early Career Scientist and Engineer Awa…
• Alumni Engineering Council Research Award, Junior Faculty -…