Silvera0218 - Overview

Hi, I'm Silvera.

I am a Master's student in Mathematics at the University of Macau, specializing in Elliptic Equations (PDEs), specifically focusing on problems of the De Giorgi type. My path to mathematics was interdisciplinary; before my undergraduate studies in math, I studied Food Science, Biology, and Bioinformatics.

Beyond my core research, I am an enthusiast of Fluid Dynamics, Differential Geometry, and General Relativity. My main passion is bridging the gap between complex mathematical theory and real-time, interactive visualization.

I’m interested in physically-accurate simulations of astrophysical phenomena and science fiction concept realizations.
I’m self-learning GLSL and ModernGL to trace light through curved spacetime.
How to reach me: [mc45151@um.edu.mo]

Astrophysical Simulations

1. Interactive Kerr Black Hole Simulator

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.

2. Real-time 3D Wormhole Ray-Tracer

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.

Computational Physics Simulations

3. 2D Incompressible Fluid Dynamics Simulator

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.