
New Member
Runge Kutta shooting with partial differential equation
I need to solve system of PDEs:
[tex]\dfrac{2}{r} \dfrac{\partial (r V_0 p_0)}{\partial r} + \dfrac{\partial (u_0 p_0)}{\partial z} =0[/tex]
[tex]u_0 \dfrac{\partial u_0}{\partial z}=\dfrac{4}{3} \beta \dfrac{\partial^2 u_0}{\partial r^2} \dfrac{\partial p_0}{\partial z} +\dfrac{4 \beta}{r}\dfrac{\partial u_0}{\partial r}[/tex]
[tex]\dfrac{\partial p_0}{\partial r}=0[/tex]
[tex]u_0 _{r=1}=0[/tex], [tex]p_0_{z=0}=p_{0i}[/tex], [tex]p_0_{z=1} = 1 [/tex]
where u_0, V_0, p_0 are dimensionless velocity in z axis, dimensionless radial velocity, and dimensionless pressure. z=0 is inlet and z=1 is outlet of this circular microtube with linear change of geometry ( [tex]r(z)=r_iz(r_11)[/tex] ), where r is radial coordinate.
I need to solve this system to get velocities and pressure, but I dont know how.
With Runge Kutta shooting methods I have different differentials, and couple of them in equations, so how to calculate these values for unknown boundary conditions?
And how to solve these eqautions later?
Last edited by mmm4444bot; 02152018 at 02:56 AM.
Reason: fixed LaTex issues
Tags for this Thread
Posting Permissions
 You may not post new threads
 You may not post replies
 You may not post attachments
 You may not edit your posts

Forum Rules
Bookmarks