How to map a domain changing in length with time
I have a problem with my CFD project and need help. The problem is I have a 1-D domain which is given by
and I try to map it into a domain that has one fixed length by using fixed number of grid points at all times. I need to find a mapping function. Thanks for your concern
If I understand this correctly, you need a 1D domain of fixed length where only the nodes change position in time? So in your simulation you would get that some cell faces are elongating while others or shortening, yet the sum of lengths is constant in time.You could start with a simpler example, by having an uniform motion of nodes:
for i = 0:N
loc_0(i) = L * i/N + L_0
for t = 0:T_end
for i = 1:N-1
loc(i,t) = loc_0(i) + L/N*sin(w*t)
This would get your nodes to move uniformly to the right and back. If this is not want you meant, please post some additional information!
the domain can be considered as 1-D engine piston. I have to figure out an algebraic function that maps the current domain in a constant length one by using constant number of grid points.
maybe i misunderstand you, but that should be easy:
you know your domain size (physically) at each time t, so just map that your unit interval as a function of t ....
your domain length is some fct of t: L(t), with a=X(x=0) and b=X(x=L(t))
so your projection is just:
[0,1]-> [a,b(t)] with equidistant nodes....
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