- #1
pcjl
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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
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