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However, your system is intrinsicly coupled, you can use several methods to solve it 
I know about the energy equation to solve for pressure.
Right now I just need to know how to approach solving these two equations in the form that they are and with only rho and v the variable. Can you name some of these methods please? Thanks! 
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and look at the PISO method 

Hi again,
I just had a look at some books and articles and from what I understood correction methods such as PISO and SIMPLE are used when the pressurebased approach is used in solving compressible flows. When using densitybased approaches are used there is no need to use these equations we have the continuity equation. I was wondering if you could correct me if I'm mistaken about this and also how I can go on about solving these equations using when using the densitybased approach? I hope u see this message. Thanks again. 
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