CFD Code Repo

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This repo contains the basic CFD Codes for 1D and 2D Problem (Stationary and time dependent problem)

2D Elliptic and Parabolic PDE's

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$u_t - \epsilon \Delta u = f$

Heat Transfer Problem

$u_t - \epsilon \Delta u = f$

$u = 0$ at $y=1$

Periodic Forcing Function

$u_t - \epsilon \Delta u = f$

$u = 0$ on all Boundaries

$f(x,y,t) = sin( 2\pi x) * sin(2 \pi y) * sin(2 \pi t)$

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1D hyperbolic PDE

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$u_t + \alpha u_x =f$

The stability of the following schemes have beeb studied for various CFL numbers

• Crank Nicholson
• FTBS - Forward in Time , Backward in Space
• BTBS - Backward in Time, Backward in Space (Implicit)
• CTCS - Central in Time Central in Space (Leap Frog)

CFL = 0.5

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Crank Nicholson

FTBS

CTCS

BTBS

Summary :

CFL = 1

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Crank Nicholson

FTBS

CTCS

BTBS

Summary :

CFL = 2

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Crank Nicholson

FTBS

CTCS

BTBS

Summary :

Overall Plot