I am a PhD researcher working at the intersection of computational fluid dynamics (CFD), classical numerical analysis and scientific machine learning. My work philosophy is verification first: every solver I publish is checked against exact analytic references, independent formulations, or hand-computed cases — with measured errors, honest limitations and reproducible pipelines, never unverified claims.
Lattice-Boltzmann and finite-volume methods, spectral solvers for the Navier–Stokes equations, shock-capturing schemes with exact Riemann references.
Physics-informed neural networks (PINNs) on ODE/PDE benchmarks with free exact solutions; proper orthogonal and dynamic mode decomposition verified against known synthetic spectra.
Adaptive quadrature, bracketed root finding, Levenberg–Marquardt inversion, sensitivity analysis and Kalman filtering — each with roundoff-level cross-checks.
Twenty original, independently verified open-source repositories. A selection:
Strictly de-aliased vorticity–streamline formulation with RK4; Taylor–Green benchmark at the floating-point roundoff floor and a 3/2-rule padded reference match to 1e-12. Delivered as a tested package plus an executed notebook.
First-order Rusanov and second-order MUSCL/SSP-RK3 finite-volume solver verified against an exact Newton-iteration Riemann solver; measured convergence orders 1 and 2.
D2Q9 BGK solver with Guo forcing and half-way bounce-back; emergent Poiseuille profile matches the analytic parabola with measured second-order grid convergence.
Hard-IC versus soft-IC initial-condition handling under identical budgets and controlled seeds, on a droplet law with a free exact solution.
Richardson-error-controlled adaptive quadrature with honest termination statuses and a bounded, regression-guarded benchmark driver.
Joseph-form updates with chi-square consistency (NIS/NEES) and the iterated Riccati gain validated against the closed-form steady-state solution — zero dependencies.
Research on verified numerical solvers for flow physics and physics-informed learning; author of twenty independently tested open-source scientific codes.
Coursework and projects in fluid mechanics, heat transfer, numerical analysis and scientific computing.
A full curriculum vitae is available on request and will be posted here as a PDF.
Best reached through GitHub: github.com/Khalil-Work.