Welcome to the Matrix

Haroot Pashayan

Computational
Fluid Dynamics

Navier-Stokes Solver & Numerical Analysis | Dr. Pashayan

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The Core Mathematics

Dr. Pashayan's work focuses on the numerical solution of the Navier-Stokes equations for compressible and incompressible flows.

01. Continuity

∂ρ/∂t + • (ρv) = 0

Describes the conservation of mass in the fluid medium.

02. Momentum

ρ (∂v/∂t + v)v = -p + μ2v + f

The heart of fluid dynamics: relationship between stress and strain rate.

03. Energy

∂E/∂t + • (Hv) = 0

Governs the conservation of total energy within the flow field.

04. Divergence Free

• u = 0

Constraint for incompressible flow simulation (Mass Conservation).

Real-Time Simulations

See the Pen Neptune Demo by Arutyun Pashayan (@h4root) on CodePen.

Interactive rendering of different fluid states. Click and drag on the canvases above to interact with the advection-diffusion solver.

Simulation: Density Advection
Standard smoke simulation using divergence-free vector fields.
Simulation: Thermal Convection
Hot color palette representing temperature gradients in high-Re flows.
Simulation: Chemical Diffusion
Cold color spectrum simulating chemical reactions or quantum fluids.

Dr. Pashayan

BS Astrophysics BA Computational Math

PhD in Applied Mathematics Computational Physics

Dr. Pashayan specializes in high-performance computing (HPC) and numerical methods for solving partial differential equations (PDEs). With over 15 years of experience in academic and industrial research, he has developed robust solvers for multi-phase flow simulations.

His current work involves optimizing the Navier-Stokes solver for GPU architectures, significantly reducing computation time for complex boundary condition problems. This website serves as a digital portfolio showcasing his research papers, code repositories (h4root), and interactive fluid visualizations.

Before academia he was the webmaster of the #1 tennis eshop Racket Doctor Inc. After academia, He worked at Pragmatic Solutions on America's Army FPS Game Client. He then lead the low latency data team at Atgames in El Segundoi in collaboration with TellTale Games in San Francisco Bay Area. He led Clicktool Inc, where they lead Marketing online. Worked on backend Api, and Fixed EvovleHealth App that was featured on Apple's website and TV Show. Now at XYZ Shop LLC he modeles turbulent flows for next-generation design which can be utilized for Tesla or SpaceX design for example.

Skills & Technologies

ASM / C / CUDA Python (NumPy/SciPy) OpenFOAM / Ansys MATLAB WebGL / Canvas Node / Java Linux / MacOS BGP / TCP / UDP LLMs / Ai / MLX Logic Design