Resources

Nonlinear Systems

Book: Nonlinear Systems, Hassan. K. Khalil, Third Edition.

Data-driven modeling

1. 1. Singular Value Decomposition (SVD)

      1. Lecture: The Singular Value Decomposition (SVD) by Nathan Kutz

      2. Singular Value Decomposition (SVD): Mathematical Overview by Steve Brunton

   2. Principal Component Analysis (PCA)

      1. Principal Component Analysis (PCA) by Steve Brunton [Matlab]

   3. Dynamic Mode Decomposition (DMD)

      1. Dynamic Mode Decomposition (Theory): The first explanation of what exact DMD does by Nathan Kutz

      2. Dynamic Mode Decomposition (Overview) by Steve Brunton

         1. PyDMD: a Python package for DMD (review introduction at https://www.youtube.com/watch?v=v33cL3o2Yuk)

      3. Physics-Informed Dynamic Mode Decomposition (PI-DMD)

CFD Frameworks

1. Dedalus

   • spectral method (high-order accuracy)

   • only simple domain system

   • can research ECS

   • adjoint feature for optimization [paper]

2. OpenFOAM

• Finite volume method 

• Flexible system and complex geometries

3. AMReX

• native AMR with block-structured mesh

4. Nek5000

• element spectral method (high-order accuracy)

• can research ECS

• Snek5000: Python framework for Nek5000

5. Oceananigans.jl 

• Finite volume method 

6. OpenLB

• Lattice boltzmann method

7. Palabos

• Lattice boltzmann method

Optimization

1. Gradient-based optimization

2. Adjoint method for compute sensitivity instead of gradient

3. Multi-objective optimization

• eg. composite objective function for airfoil

Optimization Frameworks

1. SU2

• Incompressible/compressible flows (subsonic to supersonic).

• Includes the flow solver, the adjoint solver, and a mesh deformation tool.

• Python wrapper (pySU2)

• Test cases https://github.com/su2code/TestCases 

2. MACH-Aero

• a framework for performing gradient-based aerodynamic shape optimization

3. DAFoam

• Discrete Adjoint for OpenFOAM

• Uses PETSc library and Automatic Differentiation

• Python interface (dafoam)

PETSc libraries

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