PhD-Track Learning: Fluid Mechanics & Numerical Simulation
“An 8-week intensive roadmap for a Masters graduate to master the theoretical and computational foundations of fluid mechanics, preparing for PhD-level research. The curriculum progresses from advanced continuum mechanics to implementing and analyzing complex CFD simulations.”
Module 1: Advanced Mathematical & Physical Foundations
By the end of this module you will be able to derive and analyze the governing equations of fluid motion using tensor calculus and scaling analysis.
Module 2: Discretization & Numerical Solvers for PDEs
By the end of this module you will be able to implement a finite difference solver for a model PDE and analyze its stability and accuracy.
Module 3: Incompressible Flow Simulation
By the end of this module you will be able to implement a basic incompressible Navier-Stokes solver using a pressure-projection method.
Module 4: Compressible Flow & Shock Capturing
By the end of this module you will be able to implement a numerical scheme capable of capturing shock waves in 1D compressible flows.
Module 5: Mesh Generation & Open-Source CFD
By the end of this module you will be able to generate a high-quality mesh for a complex geometry and set up a basic simulation case using OpenFOAM.
Module 6: Turbulence Modeling
By the end of this module you will be able to select, implement, and critically evaluate an appropriate RANS model for a turbulent flow problem.
Module 7: High-Performance Computing (HPC) for CFD
By the end of this module you will be able to decompose a CFD problem for parallel execution and analyze its scaling performance.
Module 8: Research Proposal & Literature Review
By the end of this module you will be able to formulate a viable PhD-level research question and outline a numerical methodology to address it.
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