Discretization Basics with variable dx

Given Problem:- Apply Reynold\'s decomposition to the NS equations and come up with the expression for Reynold\'s stress. Explain your understanding of the terms Reynold\'s stress What is turbulent viscosity? How is it different from molecular viscosity?   Solution:- NAVIER STOKES- The movement of fluid in the physical…

Given Problem:- Phase 1: Geometry cleanup Cleanup the 48 errors Flag the front wings, rear wings, tyres, suspension links as separate boundaries Create a virtual wind tunnel Ground plane reference is provided in the lower end of the tyres. There will be a \"flat section\" in all the 4 tyres. This refers to the location…

Its OCTAVE CODE. clear all; close all; clc; %analytical function=sin(x)/x^3; %analytical derative:- % f\'(x)= ((x^3*(cos(x)))-(sin(x)^3*x^2))/x^6; x=pi/3; analytical_derivative=((x^3*(cos(x)))-(sin(x)*3*x^2))/x^6; %Numerical Derivative %Forward differencing(First Order Approximation) %(F(x+dx)-F(x))/dx dx=pi/40000, forward_differencing=(((sin(x+dx))/(x+dx)^3)-((sin(x))/x^3))/dx;…

We have Plottes 3 errors namely:- 1. First order error 2. Second Order Error 3. Fourth Order error All these errors have different error values due to different trunkation error due to order of approximations. Fourth order approximations is most near to the actual analytical answer. Hence we post different graphs to show…

Its OCTAVE CODE. clear all; close all; clc; %analytical function=sin(x)/x^3; %analytical derative:- % f\'(x)= ((x^3*(cos(x)))-(sin(x)^3*x^2))/x^6; x=pi/3; analytical_derivative=((x^3*(cos(x)))-(sin(x)*3*x^2))/x^6; %Numerical Derivative %Forward differencing(First Order Approximation) %(F(x+dx)-F(x))/dx dx=pi/40000, forward_differencing=(((sin(x+dx))/(x+dx)^3)-((sin(x))/x^3))/dx;…

Given Problem:- Create the CAD model using your any CAD package (50 points) Setup a Coarse CFD simulation (300 points) Setup the virtual wind tunnel as shown in the video Apply the right boundary conditions and solver settings (50 points) Use a coarse mesh to demonstrate that your setup runs successfully (150 points).…

Given Problem:- Simulate flow over a 4 digit airfoil i.e NACA 2412 Airfoil. You will have to calculate the following, Drag co-efficient Vs Angle of Attack Lift co-efficient vs Angle of Attack Compare the effect of turbulence models on the above two results. Make sure that the inlet Reynolds number is 200,000 Make…

Given Problem:- Setup a flow simulation through a pipe Inlet Reynolds number should be 7,000  Add Y+ to your post.in file Start with an initial base grid Run grid dependence test on 3 grids and show that the outlet temperature converges to a particular value Effect of supercycle stage interval Set supercyle stage…

Given Problem:- Setup a transient shock tube simulation Plot the pressure and temperature history in the entire domain - Explain the result Plot the cell count as a function of time - Explain the result Software used- 1. Converge CFD Software 2. Cgywin 3. Paraview Geometry - Steps Involved while solving this challenge-…

Given Problem:- 1. Shock flow boundary conditions Do a literature search on what BC\'s are typically used for shock flow problems 2. What is a shock wave? In your own words, describe the physics behind shock waves 3. Effect of SGS parameter on shock location In the Prandtl Meyer shock problem, look at the effect of SGS…

Given Problem:- Q. Simulate Flow of fluid over a throttle body in converge studio and post process the results Software used- 1. Converge CFD Software 2. Cgywin 3. Paraview Throttle body Step design-     Steps Involved while solving this challenge- 1. We first download the required geometry from the website…

Given Problem:- Q. Simulate Flow of fluid over a throttle body in converge studio and post process the results Software used- 1. Converge CFD Software 2. Cgywin 3. Paraview Throttle body Step design-     Steps Involved while solving this challenge- 1. We first download the required geometry from the website…

Given Problem:- Q. Channel flow simulation using Converge CFD Software used- 1. Converge CFD Software 2. Cgywin 3. Paraview   Backward Facing Step design- Steps Involved while solving this challenge- 1. Create the desired geometry in the converge cfd software using its CAD tools. For this challenge we will make…

Given Problem:- Q. Channel flow simulation using Converge CFD Software used- 1. Converge CFD Software 2. Cgywin 3. Paraview   Design of Channel using Converge- Steps Involved while solving this challenge- 1. Create the desired geometry in the converge cfd software using its CAD tools. For this challenge we will…

Interpolation Schemes : InterPolation is a process in which we use points with known value and sample points to estimate values at others unknown points.  In FVM, interpolation schemes are used to find values of volume integrals required at the points other than nodes. Some of these schemes are:- 1. Upwing interpolation…

Fourth order approximations of the second order derivative using the following schemes are derived with the help of Programming:- Central difference Skewed right sided difference Skewed left sided difference MATLAB code for solving all these 3 types of approximations:-   %------------------------------------------MATLAB…

Given task- In the previous part we looked into the simulation results for a laminar, incompressible flow through a pipe in OpenFOAM. Now in this section, we would attempt the same problem with the symmetry boundary conditions.    MATLAB Script to create blockMeshDict file The program will be same like wedge…

Given- Reynolds number based on pipe diameter and inlet velocity should be 2100 Working fluid - water You need to calculate the length of the pipe Calculate length of the pipe using the entry length formula for laminar flow through a pipe Show that entry length is sufficient to produce a fully developed flow. You will…

Objective- Simulate the mtion between 0-20 sec, for angular displacement=0,angular velocity=3 rad/sec2 at time t=0. 1. You have to upload the animation on Youtube and paste the link to your answer. 2. Upload the code using \"INSERT SAMPLE CODE\" option and then post screenshot of the plots generated.   ODE used- …

Objective- For the follow diagram, use the icoFOAM solver to simulate the flow through a backward facing step. You will be creating multiple meshes and will be comparing the results obtained from each mesh.   Creating The Given shape:- 1. Open the Tutorial file in open foam. 2. Go to incompressible folder and then…

Given Problem:- Our objective in this project is to write code solve the 1D supersonic nozzle flow equations using the Macormack Method. You will be implementing both the conservative and non-conservative forms of the governing equations You will perform grid dependence test Write separate functions for conservative and…

1. Divergence- It is used to tell us about net fluid flow in an given condition. It tells us about that whether the fluid is flowing from a source (in this case it is positive)and if the net fluid is entering into the source than the divergence will be negative. e.g. is attached in link. 2. Gradient- gradient basically…

1. Divergence- It is used to tell us about net fluid flow in an given condition. It tells us about that whether the fluid is flowing from a source (in this case it is positive)and if the net fluid is entering into the source than the divergence will be negative. e.g. is attached in link. 2. Gradient- gradient basically…

1. A=(1,2,3,4,5) signifies the array with given values of array A. All these number are given by the operator and he can use them for calculation. It will create an Matrix. 2. B=[1;2;3;4;5]-  It will create a [1X5] matrix i.e. 1 row and 5 column of 1 to 5. 3. C=A*B\'- It will create an output error as both B and A…

 Following prerequisite for the question is already given i.e. Grid points(n)=80; Time steps(dt)=1e-4, 1e-3, 1e-2, and 1e-1; This question is second part of Linear convection equation in which we are doing time marching to obtain the solution after some specific given time. Now we have got 4 time steps,so we are going…

As the problem state that we need to show the effect of number of moles of carbon on the stiochemetric co efficient \"ar\", we are going to use arthemetic mean to solve the calculation for the purpose of solving it. The given equation will be break apart to solve the value of \"ar\" for different values of moles. We all…

1. A=(1,2,3,4,5) signifies the array with given values of array A. All these number are given by the operator and he can use them for calculation. It will create an Matrix. 2. B=[1;2;3;4;5]-  It will create a [1X5] matrix i.e. 1 row and 5 column of 1 to 5. 3. C=A*B\'- It will create an output error as both B and A…

Given Problem Statement- Solve the 2D heat conduction equation by using the point iterative techniques:- Implement the following methods 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation Absolute error criteria is 1e-4   Problem :1. The domain is a unit square.2. The number of points along the…

Given Problem Statement- Solve the 2D heat conduction equation by using the point iterative techniques:- Implement the following methods 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation Absolute error criteria is 1e-4   Problem :1. The domain is a unit square.2. The number of points along the…

Given Problem Statement- Solve the 2D heat conduction equation by using the point iterative techniques:- Implement the following methods 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation Absolute error criteria is 1e-4   Problem :1. The domain is a unit square.2. The number of points along the…

Fig.1, For n=20     Fig.2,for n=40   Fig.3,for n=80   Fig.4,for n=160   https://docs.google.com/document/d/1kHpnufcZ2pa0EpaUMzqJLjm3ueBC1gol4PWjchnxPOY/edit?usp=sharing   Understanding of Plots:-   1. Figure1(n=20)-   Red line plot is original plot without time marching. Blue line…

Boundary and Initial condition are way to imporatant as PDE have infinite solution and to find the unique or desired solution for our PDE equation we need to define its boundary and initial conditions.  We need to define a domain for a specific 1d or 2d aspect , like for nozzle or diffuser. In that domain we define…