Krunal Panchal.

Computational methods for complex physical systems — combustion kinetics, optimization & uncertainty quantification, reduced-order & scientific ML.

Under the hood

The solver behind the flow

The hero is a 2D incompressible flow solved on the GPU every frame (WebGL2, stable-fluids scheme). Below: the equations, the matrix its pressure step inverts, and live numbers from the running simulation.

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1. The equations

Incompressible Navier-Stokes for velocity u and pressure p:

∂u/∂t + (u·∇)u = -∇p/ρ + ν∇²u + f, ∇·u = 0

The solver advances one time step in three stages, in this order: force (vorticity confinement, buoyancy, inflow, your pointer), project (make the field divergence-free), advect (MacCormack semi-Lagrangian). There is no explicit ν∇²u term: viscosity here is the numerical diffusion of the advection step plus a small linear decay.

u* = u_n + Δt f

∇²p = (ρ/Δt) ∇·u*, u = u* - (Δt/ρ) ∇p

u(x, t+Δt) ≈ u(x - Δt u, t)

On the grid (spacing h) the Laplacian is the 5-point stencil, one linear equation per cell:

(p(i+1,j) + p(i-1,j) + p(i,j+1) + p(i,j-1) - 4p(i,j)) / h² = b(i,j)

b(i,j) = (ρ/Δt) (u*(i+1,j) - u*(i-1,j) + v*(i,j+1) - v*(i,j-1)) / 2h

2. The matrix it solves

Stacking all cells gives a sparse linear system A p = b. Each row has at most five nonzeros: the diagonal and the four neighbours (+1). Hero boundaries: left, top and bottom are zero-gradient walls (the missing neighbour is replaced by the cell itself, so the diagonal becomes -3 or -2); the right edge is an outlet with p = 0 (diagonal stays -4, no right neighbour).

Grid

Hover or focus the matrix (arrow keys) to read an entry.

diagonal (-4, -3, -2)
neighbour (+1)
zero

The solver does not factorise A. It runs a fixed number of Jacobi sweeps per frame (see iterations below), warm-started from last frame's pressure times 0.8. In the shader the units are h = 1 and p is scaled by Δt/(ρh), so ρ and Δt drop out:

p_new = (p_L + p_R + p_B + p_T - b) / 4

b = ½(u_R - u_L + v_T - v_B)

With general spacing the update is p_new = (p_L + p_R + p_B + p_T - h²b)/4. At a wall the shader substitutes the cell's own value for the missing neighbour, so those rows iterate p ← p - (b - A p)/4. After the sweeps the velocity is corrected with a central difference:

u ← u - ½(p_R - p_L, p_T - p_B)

The cylinder and the hot burner act as extra zero-gradient interior walls; the demo matrix above leaves them out.

3. Live numbers from the running hero

Reading the simulation.

What each number means

Sim grid: Cells of the velocity and pressure grid (width × height). The picture is drawn at a higher resolution than this.
Quality tier: 0 is highest, 3 lowest. The hero lowers it automatically if frames take too long.
Jacobi sweeps / frame: How many times the pressure update above is applied each frame. More sweeps leave less divergence.
Frames per second, frame interval: Measured between browser animation frames, so it is capped by the display rate. It is not GPU time.
Time step Δt: Seconds advanced per step: the frame interval, clamped to 1/120 - 1/30 s.
CFL number: Δt · max|u| / h, the number of cells the fastest fluid crosses in one step, using the speed after the solve. Semi-Lagrangian advection stays stable above 1.
max |∇·u| before / after: Largest divergence of the velocity field over the whole grid (boundary cells included), in 1/s: the field entering the pressure solve versus the field leaving it, sampled once a second from the GPU in 8 × 8 cell blocks. After is not zero: a fixed number of sweeps solves A p = b only approximately. Advection, applied afterwards, is not included.

Numbers shown come from the solver in this tab; nothing is sent anywhere.

PhD, Mechanical Engineering, IIT Madras (2026)Project Associate, Dept. of Mechanical Engineering, IIT Madras, until 30 Nov 2026

I build computational methods that connect detailed chemical models with practical combustion applications — kinetics, mechanism reduction, fair multi-objective optimization, uncertainty quantification, and scientific ML, treated as one connected problem rather than separate tools. Every figure on this site is backed by real runs — pool-flame experiments measured with instruments I built, stiff autoignition chemistry validated against 426 experimental targets, an open-source optimization workbench, and a live Neural ODE research playground — with the honest failures on record next to the results. The full story →

Overview

Research at a glance

Combustion Kinetics & Mechanism Reduction — mechanism development, validation, and reduction of detailed kinetic models to tractable, simulation-ready form
Experimental & Numerical Combustion — pool-flame characterization and downdraft gasification alongside CFD and chemical-kinetics simulation of the same systems
Fair Multi-Objective Optimization & Uncertainty Quantification — multi-stage, multi-dataset calibration of Arrhenius parameters with correlated-parameter Bayesian UQ, built around MOSIAC, my open-source optimization framework
Reduced-Order Modelling & Scientific ML — neural and response-surface surrogates that stand in for expensive stiff simulations
Gasification — steam/catalyst-assisted downdraft fixed-bed gasification, from rig commissioning to syngas analysis
CFD — PANSOPHIA, an in-house CFD/multiphysics solver, and reacting-flow and rig-design studies built on top of it
Optimization & Reinforcement Learning — dokimazo, an open-source, dependency-light optimization/RL workbench with a plug-and-play graph IR — closed with an RL agent that tunes a real molecule’s rotatable bonds to find its lowest-energy 3D shape

The full research overview — themes, methods, experiments, and publications — is on the Research page.

Combustion12 Optimization8 UQ4 SciML6 CFD8 Experimental3 Visualization4 Software1 Education4 Photonics3 Electronics8 Apps2

projects: 40
images: 588
videos: 100
studio routes: 24
categories: 12

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Showcase

Selected work

A rotating sample of the best results across every research area — each slide links to its full project page. Browse all projects →

Four regimes, tracked live, one frameflamelab — ignition through periodic flickering, width tracked at multiple zone heights at once, in real timeOpen project

Four sampling methods, live, one frameMUQ-SAC — all four sampling-method classes building their uncertainty bands at once, each at its own real measured speedOpen project

3D ignitability map: MOSIAC — ignitable vs. non-ignitable conditions across T, P and equivalence ratio — **3D ignitability map**MOSIAC — ignitable vs. non-ignitable conditions across T, P and equivalence ratioOpen project

Fair objective-function design: MSO objectives — WMRE vs. power-mean behaviour, the optimizer's own objective library — **Fair objective-function design**MSO objectives — WMRE vs. power-mean behaviour, the optimizer's own objective libraryOpen project

Symbolic regression for rate rules: PySR — collinearity diagnostics for universal rate-rule discovery — **Symbolic regression for rate rules**PySR — collinearity diagnostics for universal rate-rule discoveryOpen project

The 115-run seed-noise floor: SciML — bootstrapped ranking with the seed-noise band that humbles most hyperparameter effects — **The 115-run seed-noise floor**SciML — bootstrapped ranking with the seed-noise band that humbles most hyperparameter effectsOpen project

12 optimizers, one race: Neural ODE playground — all 12 gradient optimizers trained from scratch, same seed, same budget — **12 optimizers, one race**Neural ODE playground — all 12 gradient optimizers trained from scratch, same seed, same budgetOpen project

Hot-spot ignition: PANSOPHIA — a warm patch reaching a tipping point and turning into a self-sustaining flame — **Hot-spot ignition**PANSOPHIA — a warm patch reaching a tipping point and turning into a self-sustaining flameOpen project

Steam-catalytic gasification: gasification — a real flame over the downdraft gasifier, from rig commissioning to syngas — **Steam-catalytic gasification**gasification — a real flame over the downdraft gasifier, from rig commissioning to syngasOpen project

H₂/CH₄ co-injection in tuyeres: decarbonisation — blast-furnace tuyere co-injection study for lower-carbon ironmaking — **H₂/CH₄ co-injection in tuyeres**decarbonisation — blast-furnace tuyere co-injection study for lower-carbon ironmakingOpen project

Vaporizer & combustion rig design: vaporizer-rigs — design and fabrication comparison across rig generations — **Vaporizer & combustion rig design**vaporizer-rigs — design and fabrication comparison across rig generationsOpen project

01 / 11

Showcase

Selected results

Flame development across eight repeat n-heptane pool-flame runs, ignition-aligned and shown at a common physical scale — measured with flamelab, the computer-vision instrument behind it (animated overlay videos on the project page). Open project
All four MUQ-SAC sampling-method classes (A, B, C, D) building their joint-uncertainty bands at once, each panel's own real measured compute time ticking at its true rate — one crawls, three finish almost instantly — see MUQ-SAC. Open project
An RL agent and dokimazo's own IPOP-CMA-ES both independently reach n-dodecane's true global-minimum conformer energy, verified against a directly-computable structural ground truth — see dokimazo (optimization-process video on the project page). Open project

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flow_field_demo.html

value_flow_demo.html

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Latest

News

Aug 06, 2026	Three abstracts accepted for presentation at the 64th Symposium (Japanese) on Combustion, Fukuoka, 4–6 Nov 2026 — including the power-mean objective-function work (Panchal & Narayanaswamy, 2026).
Jul 15, 2026	PhD degree conferred by IIT Madras.

Papers

Selected publications

CTM2024

A fast uncertainty quantification methodology and sampling technique for joint probability distribution of the Arrhenius rate expression: a case study applied to H2/CO kinetic mechanism

Krunal Panchal, Vaisakh Vasudavan, Sivaram Ambikasaran, and 1 more author

Combustion Theory and Modelling, 2024

DOI BibTeX

@article{panchal2024muqsac,
  title = {A fast uncertainty quantification methodology and sampling technique for joint probability distribution of the Arrhenius rate expression: a case study applied to H2/CO kinetic mechanism},
  author = {Panchal, Krunal and Vasudavan, Vaisakh and Ambikasaran, Sivaram and Narayanaswamy, Krithika},
  journal = {Combustion Theory and Modelling},
  volume = {28},
  number = {4},
  pages = {411--440},
  year = {2024},
  doi = {10.1080/13647830.2024.2326413},
}

2023

A multi-stage kinetic reaction optimization strategy applied to n-heptane combustion mechanism

Krunal Panchal, Vaisakh Vasudavan, and Krithika Narayanaswamy

In 14th Asia-Pacific Conference on Combustion (ASPACC), 2023

BibTeX

@inproceedings{panchal2023aspacc,
  title = {A multi-stage kinetic reaction optimization strategy applied to n-heptane combustion mechanism},
  author = {Panchal, Krunal and Vasudavan, Vaisakh and Narayanaswamy, Krithika},
  booktitle = {14th Asia-Pacific Conference on Combustion (ASPACC)},
  year = {2023},
}

Accepted2026

A Power-Mean (Hölder) Objective Function for Balancing Unequal Datasets in Combustion Kinetic Mechanism Optimization: Case Studies on Methyl Butanoate and n-Heptane

Krunal R. Panchal and Krithika Narayanaswamy

In 64th Symposium (Japanese) on Combustion, 2026

Accepted