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CFD Discretization Help Needed

  1. Jul 14, 2012 #1
    Hi guys I was wondering if anyone on here could help me out.

    Essentially I am trying to build a higher order cfd code and struggling to work out where to start, I’m trying to build it using polynomial fitting so here’s my problem.

    Taking my domain as;

    ϕ_(i-2)------------------ϕ_(i-1)------------------ϕ_i------------------ϕ_(i+1)
    |------------------------|----------------------|---------------------|
    x=0---------------------1/3 --------------------2/3------------------x=1

    So I’m wanting to fit a 3rd order polynomial however I’ve not really done much polynomial fitting since A level so I’m quite stuck, here’s what I have,

    ϕ=ax^3+bx^2+cx+d

    Taking the infomation from the domain I can get the four equations

    ϕ_(i+1)=a+b+c+d

    ϕ_i=a(2/3)^3+b(2/3)^2+c(2/3)+d

    ϕ_(i-1)=a(1/3)^3+b(1/3)^2+c(1/3)+d

    ϕ_(i-2)=d

    My problem is that there seems to be two many unknowns can anyone help
     
  2. jcsd
  3. Jul 15, 2012 #2

    AlephZero

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