outflow boundary contition
Hi!
i need some help with an outflow bc. i am writing an 1D code for a flow in a duct. i am using 1D finite volume equations and an crank nikolson method. at the last node "n" (exit flow node) i need a bc because i do not know the "n+1" node. i found that one proper boundary contrition is the DT/dt + v*DT/dx =0 (1) (I am solving only the energy equation). what i'd like to ask is that in my me equation which is in form A(n,n1)Tn1(t+dt) + A(n,n)Tn(t+dt) + A(n,n+1)Tn+1(t+dt) = B(n,n1)Tn1(t) + B(n,n)Tn(t) + B(n,n+1)Tn+1(t) i have to terms that i do not know the Tn+1(t+dt) and the Tn+1(t). to do this i have to solve the (1) two times one implicit and one explicit so to replace the two above terms ? thanks 
Y don't U use CFD softwares?

I am using cfd. the purpose of the code that i make is to speedup the cfd calculations

which program U write codes with? I just know some fortran 90.

I am also using fortran 90.
i found that the vdT/Dx = 0 seems to work good. but i don't know if this is the best BC 
Sorry. I don't know either.

Dear Kordou;
it seems you need basic studies in CFD. All T(t) terms,like Tn(t) or Tn+1(t) or Tn1(t), are determined either from a previous time step olution or an initial guess. if you use an implicit scheme for the term of vdT/Dx , you will have two unknown terms for each point, namely Tn(t+dt) and Tn+1(t+dt). knowing the boundary condition for first and last points, (inlet and outlet) a set of equations will be earned. solution of this set will give you the right answer. it is unconditionally stable but its solution needs more efforts.since a set of equations wil be solved simultaniously. if you use an explicit scheme, there is only one unknown term, namely Tn(t+dt), which is easily found at each point. but it is not unconditionally stable and may diverge for specific values of dt,dx and v. regards 
Dear Hamidzoka
At start thank you for the help :) Indeed I have the basic knowledge of finite element method. I have a code that uses the cranknicolson method (both implicit and explicit) to solve a system of equations (the Energy equation) in the above form (1st post here). The terms in the right of the equation at time (t) are known from either a initial guess of from a previews time step. My problem for the boundary condition (1) of the first post is not the term vDT/Dx. I calculate this as you suggest it. My problem is the that in one Boundary condition i have 2 terms, one that depends on time (DT/Dt) and the other that depents on space (vDT/Dx). If i apply only the second term as a boundady condition vDT/Dx=0 (as a read this is ok for steady state) which basically gives the same BC as DT/DX=0, my result are very good. But i have a transient code so (as i read) i have to also include the term DT/Dt (whicj is (T(n+1)T(n))/dt as well. but i have never worked on a BC both on time and space. As i said i I do not have much knowledge on cfd theory, so sorry i have said something stupid. thank you again 
Dear Kordou;
you are not permitted to descritize the energy equation in "n"th (exit flow) node as well as first (inlet flow).disctritization starts from node 2 to n1. since there is no n+1 or 0 node in domain! lets focus on BC: you have to choices for "n"th (exit flow) BC as the following: 1temperature: Tn is specified 2heat flux: Qn is specified suppose that you 've selected the temperature. therefore Tn is known. so, let review all temperature nodes at node "n1": Tn2(t+dt) : is known from previous time step or an initial guess Tn2(t) : is known from previous time step or an initial guess Tn1(t+dt) : is unknown and should be computed Tn1(t) : is known from previous time step or an initial guess Tn(t+dt)=Tn(t) : Tn is BC and assumed to be fixed. therefore it dies not change with time.(in case boundary condition of Tn varies with the time, its function should be known and therefore Tn(t+dt) is calculated using its function). you will see there is no other unknown term. does it help? Regards Hamidzoka 
Dear Hamidzoka
Your answer is quite helpful! thank you 
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