A real-time simulation of both Schwarzschild (static) and Kerr (rotating) black holes. It accurately demonstrates key General Relativity phenomena by performing numerical integration (4th-Order Runge-Kutta) on the GPU:

• Gravitational Lensing: Distorts the background starfield.
• Frame-Dragging: The "spacetime vortex" effect of the rotating Kerr hole.
• Relativistic Doppler Beaming: The bright approaching vs. dim receding disk.
• The Photon Ring: Delicate, nested rings of light at the shadow's edge.

A real-time traversable wormhole (Morris-Thorne metric) simulator. It performs "reverse ray-tracing" in a GLSL fragment shader for every pixel to accurately simulate the exotic visual distortions of passing through a wormhole.

• Physically-Accurate: Based on the analytic model from arXiv:1502.03809.
• First-Person Traversal: Full 6-DOF (six-degrees-of-freedom) camera control.
• Connects Two Universes: Links two distinct "universes" (skyboxes).
• Multiple Images: Renders the multiple "ghost images" visible inside the throat.

A robust MATLAB-based solver for the 2D incompressible Navier-Stokes equations, applied to channel flow around multiple obstacles. This project demonstrates the application of advanced numerical methods to solve complex, non-linear PDEs in fluid dynamics.

• Finite Element Method: Utilizes stable Taylor-Hood (P2-P1) elements for spatial discretization.
• Multiple Steady-State Solvers: Implements and compares Oseen, Stokes (Picard), and Approximate Newton linearization schemes.
• Unsteady Simulation: Employs a full Newton solver within each time step to accurately capture time-dependent flow.
• Captures Classic Phenomena: Successfully simulates the von Kármán vortex street for low-viscosity flows.
• Globalization Strategy: Integrates a backtracking line search with the Armijo condition to ensure robust convergence.