👋 MOHAMMED AHMED

PhD researcher (@ UCAS) · Mechanical Engineer — scientific computing, CFD, heat transfer, and numerical verification. I build small, tested solvers and estimation tools where featured claims are checked against analytic references and figures come from recorded runs.

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▶ Watch the animations

Open the full animation gallery — twelve published animations and three previews from projects still in review.

💠 Khalil Droplet Population Atlas

A bespoke addition in Droplet Journey: 16 droplet-size groups shrink under the analytic constant-K law while a liquid/vapor ledger tracks their mass. The comparison matches initial mass and D32 with a monodisperse population. 61 computed frames, raw data, equations and 25 passing project test cases.

▶ Open the animated GIF in your browser

Source, equations and reproduction. Circle positions are schematic; this is an independent-droplet benchmark.

Animation	Open the GIF
🌀 Periodic vortex dynamics	Play Vortex Notebook
⚡ Sod shock-tube waves	Play Shockline
💧 Single-droplet heating and evaporation	Play Droplet Journey
📡 State-estimation and covariance diagnostics	Play Trajectory Fusion
🎯 Native Fortran root-finding comparison	Play Bracket Root
Energy Flow Atlas	Play Energy Flow Atlas
Thermal Streams	Play Thermal Streams
Pipeflow Bench	Play Pipeflow Bench
Variance Compass	Play Variance Compass
Channel Lattice	Play Channel Lattice
Droplet PINN Studio	Play Droplet PINN Studio

If your app shows a still preview, tap Open the animated GIF and open the link in your web browser. The files are animated GIFs, rather than screenshots.

🌀 Featured result — Vortex Notebook

_{Recorded from the computed nonlinear run (N = 128, ν = 5e-4 m²/s, 41 frames): strictly de-aliased 2D spectral Navier–Stokes. Taylor–Green verification error sits at the floating-point roundoff floor (1.3e-15); RK4 convergence order measured at 4.03–4.12; the nonlinear operator matches an independent 3/2-rule padded reference to 1e-12.}

• ▶ Executable Jupyter guide — derivations + live verification cases
• 🔬 Numerical evidence — what each of the 12 tests does and does not establish
• ⚡ Quick start: pip install -r requirements-dev.txt && python -m pytest tests -q

Also verified: Shockline — conservative 1D Euler waves (first-order Rusanov + second-order MUSCL/SSP-RK3) against an exact Newton-iteration Riemann solver: exact advected-contact convergence orders 1 and 2 through N=800, published Sod star state to 5e-5, 12 tests + CI, and a 41-frame computed shock-tube animation (results).

Also verified: Droplet Journey — 0-D droplet evaporation and heating with the Spalding d²-law, correct sphere-area lumped heating, and documented threshold stops: frozen-state d² validation to 1.7e-16, agreement with an independent tight-tolerance reference below 1e-7, 25 test cases + CI, and a 41-frame dense-sampled animation (results).

📐 Verified original projects

Project	What it is	Evidence
Vortex Notebook	2D spectral Navier–Stokes (vorticity–streamfunction, strict 2/3-rule, RK4) + executed notebook	12 tests; roundoff-floor Taylor–Green; padded-reference alias check
Shockline	Conservative 1D Euler finite-volume solvers with exact Riemann benchmarks	12 tests; contact-convergence orders 1 & 2; 41-frame animation
Droplet Journey	Single-droplet evaporation/heating and the weighted Khalil Population Atlas	25 test cases; independent coupled reference; 41- and 61-frame animations
Trajectory Fusion	Native C99 Kalman filter with a documented synthetic trajectory	GCC build; NIS/NEES Monte Carlo checks; zero-noise anchor; 60-frame animation
Bracket Root	Native Fortran bracketed scalar solvers and midpoint error bounds	103 assertions; four reference equations; 13 saved CSVs; 46-frame animation
Energy Flow Atlas	Balanced power ledger and quantitative Sankey geometry	23 tests, seven transfers, fixed scale and saved frame data; 41-frame animation
Thermal Streams	Heat-exchanger rating and conditioned temperature fields	770 parametrized cases, 80-digit reference, both capacity orientations; 48-frame animation
Pipeflow Bench	Pipe friction and pressure loss with residual-based stopping	39 tests, actual solver traces and explicit transition flags; 43-frame animation
Variance Compass	Centered covariance sensitivity with row bootstrap	88 tests, affine-invariance regression and analytic Ishigami comparisons; 44-frame animation
Channel Lattice	D2Q9 channel flow with exact wall placement and Guo forcing	68 tests; independent Poiseuille benchmark; relative L2 error 2.09e-4; 62-frame animation
Droplet PINN Studio	Equal-budget hard/soft initial-condition PINNs for the normalized droplet ODE	6 CPU tests; reproduced seed-0 profile; held-out maximum absolute error 7.72e-5; 40-frame animation

(This index grows as additional original projects complete review — more are in progress.)

🤝 Contributions and bug reports

The featured verified originals above ship reproduction commands, pinned dependencies, recorded result data, and CI — if one of them does not reproduce for you, please open an issue with the exact command, your runtime versions, and the observed vs. documented numbers; that is the fastest path to a fix. Useful reports with a minimal reproducer are always welcome.

📊 Community stats

_{Community-generated public GitHub statistics from the open-source github-profile-trophy service — not official GitHub awards, engineering-quality ratings, or percentile ranks. Commit counts include the disclosed reconstructed calendar records described in those repositories.}

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🔬 Links: LinkedIn · YouTube

Calendar note: the native 2024–2026 contribution graph includes disclosed reconstructed date records.