Research

Reduced order model (ROM) for Combustion

Case study geometry and temperature sensors

SimulCaseStudy.mov

Fire Dynamics Simulator simulation of the case study

My MSc thesis supervised by Dr. Carlos Sing Long at PUC is an interdisciplinary research project focusing on the development of a reduced order model for fire forecasting. By carefully considering the relevant physics, we leverage the Boussinesq approximation and propose a Galerkin method using a Fourier basis. The truncation in this basis can be interpreted as a reduced order model that can be interpreted physically. Furthermore, we use an immersed boundary method to enforce the boundary conditions. I implemented all the code myself and it will be published un GitHub in early 2021.

ROM Fourier simulator

I implemented a ROM Fourier simulator that allows efficient simulations of the Convection equation, Unsteady Stokes equations, Navier-Stokes equations and Boussinesq equations. For the boundary conditions an immersed boundary method is utilized that allows for Dirichlet, Neumann and free boundary conditions. The user can enforce the divergence free condition that is imposed via the Fourier decomposition itself.

BoussGauss22.mp4

Boussinesq buoyancy-driven flow

Temperature source consisting of three Gaussian functions. Convection phenomena can be noted as air transports temperature.

Buoyancy-driven flow in a differentially heated closed cavity: immersed boundary method

A flow is heated from the left vertical wall with a higher temperature than the right vertical wall. Neumann boundary conditions are considered in the horizontal walls

Bouss_RK4Val3.mp4

The immersed boundary method utilizing a projection with norm L2

Bouss_RK4Val3Sobolev1.mp4

The immersed boundary method utilizing a projection with norm in H1 Sobolev space

NS_RK4Val3.mp4

Test case for Incompressible Navier Stokes with Vortex solution

Test case of simulation that utilizes a source that has an explicit solution. As can be seen the numerical scheme proposed converges to the solution. The velocity field is showed also in the extended domain and also the Fourier coefficients of its magnitude. (the Fourier coefficients for the error are mainly due to the differences in the extended domain in which the computational one is inmersed)

CD_TestMultiplePlot2.mp4

Convection simulation with homogeneus boundary conditions

Fejer Kernel with advection of velocity constant velocity fields that includes perturbation in some Fourier coefficients. The extended domain is showed and the Fourier coefficients.

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