Numerical Modeling

Solution of Poisson equation using Finite Difference Approximation
Solution of non-linear boundry value problem using Finite Difference Approximation
  • Used finite difference approximation method to discretize two-dimensional non-linear BVP and form couple of algebraic equations of the form R=0

  • Solved the equations by implementing Newton' Method

  • Tracked all the non-trivial solutions using analytical method and the arc length continuation method

  • Used finite difference approximation method and discretized two-dimensional Poisson's equation and boundary conditions in the form of Ax = b

  • Wrote MATLAB code to generate coefficient matrices 'A' and 'b' and solve for unknown 'x' using 4 different solvers:

    • Intrinsic MATLAB solver

    • LU Decomposition

    • Jacobi solver, and

    • Gauss-Seidel iterative solver

  • Generated numerical solution for the problem with different grid sizes and compared scaling behavior and errors  for these methods

Solution of Lotka-Volterra system of equations using Euler methods
  • Calculated critical points for the system of non-linear system of ordinary differential equations

  • Set up solution equation based on both intrinsic and explicit Euler methods and performed accuracy analysis by varying the step size

  • Analyzed phase plots and performed physical linear stability test

  • Worked with 2 classmates and investigated coupled heat and hydrogen transfer processes in an annular cylindrical hydrogen storage device filled with five different metal alloys

  • Adapted Finite Volume Method using central difference scheme and I wrote majority of around 1000 lines of code in C++ to simulate these transport equations

  • Studied Hydrogen storage performance by varying the operating parameters, such as, hydrogen supply pressure, cold fluid temperature and overall heat transfer co-efficient

Absorption Characteristics of Hydrogen in a Metal Hydride Bed
Skills: MATLAB, C++, R, Python, Computational Fluid Dynamics, Finite Elemet Analysis, Data Mining
Analysis of Airbnb Reviews, hosts and user preferences

Airbnb, ever since its foundation in 2008, has impacted the travel experiences of people all around the world. In this project, I collected data from various internet sources, cleaned and modified for my analysis, and

  • Predicted in which country a new Airbnb user will book his or her holiday based on information about their age, gender, nationality etc

  • Studied hosts, and analyzed occupancy of different Airbnb listings in Austin, Texas

  • Performed text mining to analyse user reviews

  • Gathered data about hotels in Texas and visualized how presence of Airbnb has impacted the revenues of these hotels, to understand the impact of Airbnb on sharing economy.

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Absorption
Absorption
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Hydrogen Storage Capacity vs. Absorption Time
Hydrogen Storage Capacity vs. Absorption Time
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Average Bed Temperature vs. Absorption Time
Average Bed Temperature vs. Absorption Time
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Hydrogen storage Capacity vs absorption time
Hydrogen storage Capacity vs absorption time
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Average Bed Temp vs absorption time in MmNi4.6Al0.4 for different overall heat transfer
Average Bed Temp vs absorption time in MmNi4.6Al0.4 for different overall heat transfer
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Hydrogen storage capacity vs time
Hydrogen storage capacity vs time
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Contour plot for num. of nodes = 5
Contour plot for num. of nodes = 5
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Contour plot for num. of nodes = 50
Contour plot for num. of nodes = 50
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Surface plot of unknown
Surface plot of unknown
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log(Matrix Size) vs. log(time)
log(Matrix Size) vs. log(time)
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Contour plot for m=1, n=1_hill
Contour plot for m=1, n=1_hill
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Surface plot for m=1, n=1_valley
Surface plot for m=1, n=1_valley
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Contour plot for m=1, n=2_hill
Contour plot for m=1, n=2_hill
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Contour plot for m=2, n=1_hill
Contour plot for m=2, n=1_hill
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Surface plot for m=2, n=3_hill
Surface plot for m=2, n=3_hill
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Surface plot for m=2, n=3_valley
Surface plot for m=2, n=3_valley
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lam_vs_nrm
lam_vs_nrm
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lam_vs_nrm_for_diff_e
lam_vs_nrm_for_diff_e
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Phase Plots with different h
Phase Plots with different h
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Species evaluation
Species evaluation
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Phase Plots
Phase Plots
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Explicit vs Implicit Euler
Explicit vs Implicit Euler
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AdamBash for h=1e-6 & Init guess=2,2
AdamBash for h=1e-6 & Init guess=2,2
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Explicit_h=1e-6_InitGuess=2,2
Explicit_h=1e-6_InitGuess=2,2
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err_vs_h_exp
err_vs_h_exp
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err_vs_h_imp
err_vs_h_imp
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Pair plot
Pair plot
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fig. 2
fig. 2
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Airbnb listings
Airbnb listings
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fig. 3
fig. 3
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Fig. 7
Fig. 7
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Fig. 16
Fig. 16
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Fig. 25
Fig. 25
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Fig. 24
Fig. 24
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Fig. 26
Fig. 26
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