Charles Naudet

Research

My research interests are applying numerical methods to many different problems of interest. Mainly, I have been involved in using numerical techniques to solve PDEs that govern some type of physics. My thesis work has been in developing novel high order methods for high-speed, shock-dominated, and time-dependent flows. Other than my thesis work, I have been involved in projects that involve biological functions, biological flows, and MEMS.

Shock tracking

My work on shock tracking aims to approximate solutions to time dependent flow problems whose solution may contain a discontinuity using coarser meshes and obtaining optimal convergence rates. My work on shock tracking includes developing methods for a space-time high-order method, adaptive mesh refinement, nonlinear solver development, and optimization methods for entropy stable flows.

Mathematical Modeling of MEMS

My work on modeling MEMS involves conducting a numerical bifurcation analysis of the post-contact states of micro electro-mechanical systems (MEMS). These problems exhibit potential for bi-stability in their systems and a difficulty in approximating their solution as they may approach a singularity. For this reason, adaptive mesh refinement is used to efficiently utilize computational resources, as can be seen in the figures to the left, refinement is localized in regions of the domain that have a sharp curvature in the solution.

Simulation based imaging

Simulation based imaging aims to use noisy pixelated data (left) that is normally obtained from MRI to reconstruct a high fidelity CFD solution (right). The CFD solution can then be leveraged to obtain better estimates of quantities of interest such as wall shear stress that is an important biomarker. Simulation based imaging uses a PDE constrained optimization approach which, in this case, optimizes the inflow boundary conditions so that the flow inside the domain most matches the noisy pixelated MRI data.

Journal Papers

  1. Charles J. Naudet and Matthew J. Zahr
    A space-time high-order implicit shock tracking method for shock dominated unsteady flows  
    Journal of Computational Physics, in review 2023
    Arxiv
  2. Charles J. Naudet and Alan E. Lindsay
    Numerical bifurcation analysis of post-contact states in mathematical models of Micro-Electromechanical Systems
    Mathematics and Computers in Simulation, in review 2023
    Arxiv
  3. Tenz Huang, Charles  J. Naudet, and Matthew J. Zahr
    High-order implicit shock tracking boundary conditions for flows with parametrized shocks
    Journal of Computational Physics (2023): 112517
    Journal, Arxiv
  4. Charles  J. Naudet, Johannes Töger, and Matthew J. Zahr
    Accurate quantification of blood flow wall shear stress using simulation-based imaging: a synthetic, comparative study
    Engineering with Computers, pp. 1–17, August 2022
    Journal, Arxiv

Conference Papers

  1. Charles J. Naudet, Brian Taylor, and Matthew J. Zahr
    High-order implicit shock tracking for finite-source spherical blast waves AIAA Aviation Forum and Exposition (Aviation 2023), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2023-3863, 6/12/2023 — 6/16/2023.
    Conference Journal