Computational Fluid Mechanics using Finite Differences method Project Work 1 -

Modify the program attached, to solve for the flow through the channel below

Assume uniform inflow and outflow, with U=1. Take viscosity so that Re=20, based on the height of the channel and inlet velocity. Notice that the top wall is a no-slip wall but the boundary condition for the bottom symmetry boundary can be taken as a full-slip wall

(a) Find the force on the object versus time.

(b) Add a code to solve the energy equation

∂T/∂t + u⋅∇T = α∇²T,

where the velocity comes from a solution of the Navier-Stokes equations. The inlet temperature is 0, the temperature at the surface of the object is 1, and the normal gradient of the temperature at the outlet, the top and the bottom are all zero. Show the temperature flux from the object versus time. Take alpha to be equal to the kinematic viscosity.

Report your results for the force as a drag coefficient and the heat transfer in terms of the Nusselt number, defined by:

Nu = (L/ΔT)(∂T/∂x)|_x=0

You should hand in a discussion of what you have done and the tests that you conducted to demonstrate the accuracy of your solution. Your report should include a printout of your code and plots of the steady-state solution (velocity vectors, pressure contours, and temperature) for at least two different resolutions. You can also compute the stream function and the vorticity.

Computational Fluid Mechanics  using Finite Differences Project Work 2 -

A Mach 3 Wind Tunnel With a Step

One of the more popular test cases for compressible flows is a shock passing though a wind tunnel with a step. The setup is described in the attached paper, in section IVb. You can write your own code from scratch using any advection scheme, or you can modify the attached scheme, originally written to simulate the Double Mach Reflection of a Strong Shock from a wedge (described in section IVc of the same paper. This program uses the Zha-Bilgen splitting and first order upwind.

You should hand in a discussion of what you have done and the tests that you conducted. Your report should include a printout of your code and plots of the solution at a few times for a few different resolutions. You can also compare with the results in the Woodward and Colella paper. Remember to be professional and concise.

I have these two projects to be done in MATLAB.

Attachment:- Assignment Files.rar