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I am currently trying to create a fortran program that will solve the flow throughout an engine manifold. I am using acoustic waves to do this.
I am NUMERICALLY solving two wave equations. one for a left propagating wave and one for a right propagating wave.
I have used all explicit schemes. Using finite differences for the spatial numerical scheme and a Runge-Kutta 4 for the time integrator. These waves simulate acoustic waves. One entering the pipe at the left, and one entering the pipe at the right.
I need to successfully apply boundary conditions (@ x=0 and x=L). When implemented correctly, these boundary conditions will transform the waves.
For example if I implement a closed wall condition. The wave should bounce of that wall and come back out. If I implement an open wave it will be inverted and sent back into the pipe as an inverted wave.
The first step of the project that I want you to do is.. implement these boundary conditions so that this happens when the programme is left to run! I dont mind if you want to do it on MATLAB, and I dont mind if you want to use your own numerical scheme. However, accuracy and stability must be ensured.
The wave shaped will be calculated from a simple analytical equation, say: exp(-200*(x-0.1)^2) and exp(-200*(x-0.9)^2). If you plot these two on a x-y graph, youll see what the waves start like. When the programme runs, the waves will approach each other at a speed of the speed of sound.
I would need an estimate of how long it will take you to do it. If its too long, then I would of probably already fixed it by then (I hope).
I cant see this being a big problem for experienced coders, and a very short task. I have more work after this. If I am impressed with this small piece of work, I will delegate more work to you (If you choose). Thank you.