Research
Senior Thesis:
High-Order Boundary Treatment for Spectral Methods [PDF , Latex] (English Version)
Linear Mesh Curved Mesh
The use of 2nd order meshes handles most spurious oscillations that appear even for well refined linear meshes.
Master Thesis:
Viscous related problems: When mesh is highly refined near the model, it is often necessary to consider the possibility that the curving process may generate invalid elements (auto-intersecting edges). The solution for this problem was handled with a Machine Learning technique, aka Radial Basis Function (RBF).
RAE2822 airfoil configuration Curved mesh with Curved mesh with
auto-intersecting cells propagated deformation
Mesh Movement: Using the same strategy, we can think of mesh movement as a Machine Learning problem, i.e.,
1. Think of the nodes of the airfoil and boundaries as a training dataset.
1.1 The airfoil has a prescribed (known) movement - say h(t) and ϴ(t)
1.2 The outer boundary has a prescribed movement - zero
2. Think of the internal nodes as the validation dataset, which you want to predict.
2.1 After you've trained your model, just predict the internal node positioning.
RAE 2822 airfoil pitching using RBF.
Next Step: Use the knowledge of RBF to add unsteady aerodynamics capacities to the code. Add geometric conservation law, metric terms, etc. Obtain results and compare with High-Order workshop test case (heaving and pitching airfoil).
Recent Published Papers:
Compressible Flow Simulations with a Spectral Difference Method Using High-Order Boundary Treatment, CNMAC 2017 [PDF]
Undergraduate Research:
2.1 Discontinuous Galerkin (DG) approximation for Burgers Equation using different shock treatments. [Formulation, Presentation, MATLAB Code, Complete Report (Portuguese)]
Main features:
Shock treatments: ENO, WENO, Constant Based Artificial Viscosity, PDE-Based Artificial Viscosity.
Legendre Polynomial reconstruction.
Viscous Flux treatment: Bassi and Rebay (BR1, BR2)
Burgers Equation solution for P = 11 DG reconstruction using 9 elements.
2.2 Legendre Polynomial Projection on 2-D Unstructured Mesh [Research Report, MATLAB Code] (Drafts - not finished; DistMesh needed)
Levantamento de coeficientes aerodinâmicos do modelo padrão AGARD no Túnel Transônico Piloto [PDF] (Portuguese Version Only)
Previously Published Papers: