Taylor table method and Matlab code Introduction to CFD using Matlab and OpenFOAM

Flux limiters are used in high resolution schemes, to avoid the aggressive oscillations  that can occur with high order spatial discretization schemes due to shocks, discontinuities or sharp changes in the solution domain.The main idea behind the construction of flux limiter schemes is to limit the spatial derivatives…

1)Creates an array A with elements 1 to 5 written in a single row of a matrix(1x5).   2)It sort of creates a transpose of the matrix A.B matrix contains 5 rows and 1 column.   3)Invalid operation: The matrix dimensions are not compatible.We need to use a . to multiply the matrix element wise.   4)Creates…

import math import matplotlib.pyplot as plt #inputs n_theta = 10 theta_start = 0 theta_end = math.pi/2 x0=0 y0=0 l1=1 l2=0.5 q=0 theta1=[] for i in range(0,n_theta): a = theta_start + i*(theta_end - theta_start)/(n_theta-1) theta1.append(a) theta2 = theta1 #print(theta1) #print(theta2) for i in theta1: for j in theta2:…

From the graph, it can be seen that the FDS and BDS methods give a higher error with decreasing dx as compared with the skewed methods. In a skewed scheme, we take into account more than one data points for calculating the data at any particular point.This helps us to get more accurate values at the desired point and hence…

https://drive.google.com/open?id=0B8mcv5CsK1aVOVJ4OXpHbTU0d2M plot code and video both 

https://drive.google.com/open?id=0B8mcv5CsK1aVNGc5ZTVGb2xBaFE From the bar graphs we can conclude that smaller time steps take longer time to process as compared to smaller time steps.Also smaller time steps tend to produce more error as compared to bigger time steps although upto a certain limit.For time step 1e-1 the…

https://drive.google.com/open?id=1jRabQ5McWgUkSOGSTRvnl_UyaAtz5ke_   Plots and code both in the drive.Cant upload the images here due to some error.

Flux limiters are used in high resolution schemes, to avoid the aggressive oscillations  that can occur with high order spatial discretization schemes due to shocks, discontinuities or sharp changes in the solution domain.The main idea behind the construction of flux limiter schemes is to limit the spatial derivatives…

https://drive.google.com/open?id=0B8mcv5CsK1aVVENNU3BCUG9RQ1k  - matlab file From the logarithmic graph that is obtained it is clear that the slope of CD4(centre difference with 4th order approximation) is the highest.hence the error associated with using this method will be less as compared to centre difference…

https://drive.google.com/open?id=0B8mcv5CsK1aVMXRIQk12a0RYSVU It is evident from the plots that as the number of grids increases the error in the solution reduces as evident from the velocity profile.However after a certain number of grid points further increase causes instability in the solution

  From the graph, it can be seen that the FDS and BDS methods give a higher error with decreasing dx as compared with the skewed methods. In a skewed scheme, we take into account more than one data points for calculating the data at any particular point.This helps us to get more accurate values at the desired…

The below plot shows how the velocity profile changes with respect to grading factor.The profile becomes more and more finer with more accurate results for 0.1 and 0.2 as the mesh gets finer and finer for these grading factors.

https://drive.google.com/open?id=0B8mcv5CsK1aVRmhjYmVFa0E1R2s

# flow over bicycle drag(force vs velocity) # flow over bicycle import matplotlib.pyplot as plt #inputs rho=1.2 A=0.1 v=[5,6,7,8,9] C_d=0.8 drag_forces=[] #Drag formula=0.5*rho*C_d*A*v*v for velocity in v: drag_forces.append((0.5*rho*C_d*A*velocity*velocity)) #print(drag_forces) plt.plot(v,drag_forces) plt.xlabel(\'Velocity(m/s)\')…

  From the graph, it can be seen that the FDS and BDS methods give a higher error with decreasing dx as compared with the skewed methods. In a skewed scheme, we take into account more than one data points for calculating the data at any particular point.This helps us to get more accurate values at the desired…

https://drive.google.com/open?id=1cvbXFmEMWEzjVqn1g1VOdZPDEvSR_Ewr

OBJECTIVE: To write a python code to compute the drag force on a cyclist and plot the respective graphs. CODE:  RESULTS: As it can be observed with higher velocities the drag force on the cyclist increases almost linearly. The drag force increases linearly with drag coefficient.