James Gabbard

About

Hello! I am a computational scientist and a doctoral candidate in the MIT Van Rees Lab working towards a PhD in Mechanical Engineering and Computation with a minor in Statistical Inference. My research focuses on computational fluid dynamics and multiphysics simulations. I work primarily with scientific software and high performance computers, developing new numerical methods and using them to simulate fluid flows with immersed solid bodies.

For a snapshot of my research, check out the links below or my Projects page.

Publications

J. Gabbard, W. M. van Rees. A high-order finite difference method for moving immersed domain boundaries and material interfaces. Journal of Computational Physics, 2024. [pdf] [doi]

J. Gabbard, W. M. van Rees. Lattice Green’s Functions for High Order Finite Difference Stencils. SIAM Journal on Numerical Analysis, 2024. [pdf] [doi]

X. Ji, J. Gabbard, W. M. van Rees. A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations. Journal of Computational Physics, 2023. vol. 494, p. 112513, 2023. [pdf] [doi]

J. Gabbard, W. M. van Rees. A High Order 3D Immersed Interface Finite Difference Method for the Advection-Diffusion Equation. AIAA SciTech Forum 2023, p. 2480. [pdf] [doi]

J. Gabbard, T. Gillis, P. Chatelain, and W. M. van Rees. An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies. Journal of Computational Physics, vol. 464, p. 111339, 2022. [pdf] [appendix] [doi]

J. Gabbard. An immersed interface method for incompressible flow with moving boundaries and high order time integration. Master’s Thesis, Massachusetts Institute of Technology, 2020. [pdf]

B. Conrey, J. Gabbard, K. Grant, A. Liu, K. Morrison. Intransitive Dice. Mathematics Magazine, Apr. 2016. [doi]

Conference Presentations

J. Gabbard, W. M. van Rees. A Performance Analysis of a High-Order 3D Immersed Interface Method Paired with a High-Order Wavelet-Based Adaptive Multiresolution Grid. SIAM Conference on Parallel Processing, Mar. 2024

J. Gabbard, X. Ji, W. M. van Rees. A high-order immersed interface method for elliptic PDEs with variable or discontinuous coefficients. APS Division of Fluid Dynamics, Nov. 2023

J. Gabbard, W. M. van Rees. High-Order Method-of-Lines Time Integration for Sharp Immersed Methods with Moving Boundaries. SIAM CSE, Mar. 2023

J. Gabbard, W. M. van Rees. A High Order 3D Immersed Interface Finite Difference Method for the Advection-Diffusion Equation. AIAA SciTech Forum, Jan. 2023

J. Gabbard, W. M. van Rees. A High-Order Immersed Interface Method for 3D Transport Equations. APS Division of Fluid Dynamics, Nov. 2022

J. Gabbard, T. Gillis, W. M. van Rees. A High-Order 3D Immersed Interface Method for Smooth Nonconvex Geometries. North American High Order Methods Conference, 2022.

J. Gabbard, T. Gillis, W. M. van Rees. Implementation and Scalability of a High-Order Immersed Interface Method on HPC Architectures. SIAM Conference on Parallel Processing, Feb. 2022

J. Gabbard, W. M. van Rees. An immersed interface vortex method for internal and external 2D flows with moving boundaries. APS Division of Fluid Dynamics, Nov. 2020