Solving a fourth order PDE

debanik1 · November 9, 2016, 15:38

Hello folks!

I have been trying to numerically solve a PDE for sometime but to no avail.

dh/dt = (1/r)*d/dr*(rh^3*PSI(r))

where PSI(r) = B*h - PHI - d2h/dr2 - (dh/dr)/r

where B and PHI are constants.

The boundary conditions are:

dh/dr(0,t)=0, d3h/dr3(0,t)=0
h(L,t)=1, dh/dr(L,t)=0

The initial condition is h(r)=Ar^4 + Br^2 + C where r belongs to [0,L].

I would be grateful if someone could help. I am a beginner in PDEs.

FMDenaro · November 9, 2016, 17:07

what is the problem you get?

debanik1 · November 9, 2016, 17:09

I am getting oscillations at the start of my domain. I would say spurious values.

The equation represents the time evolution of droplet height with radius.

FMDenaro · November 9, 2016, 17:35

Quote:

Originally Posted by debanik1

I am getting oscillations at the start of my domain. I would say spurious values.

The equation represents the time evolution of droplet height with radius.

could you attach some references?

debanik1 · November 9, 2016, 17:39

Here is the link to the paper.

https://www.cambridge.org/core/journ...1EA3FB2662BBC5

Please refer to (3.1) and (3.2).

In case you don't have access to journals, please mention your email id so that I can forward you the paper?

November 9, 2016, 15:38	Solving a fourth order PDE	#1
debanik1 New Member Choose one... Join Date: Oct 2012 Posts: 8 Rep Power: 13	Hello folks! I have been trying to numerically solve a PDE for sometime but to no avail. dh/dt = (1/r)d/dr(rh^3PSI(r)) where PSI(r) = Bh - PHI - d2h/dr2 - (dh/dr)/r where B and PHI are constants. The boundary conditions are: dh/dr(0,t)=0, d3h/dr3(0,t)=0 h(L,t)=1, dh/dr(L,t)=0 The initial condition is h(r)=Ar^4 + Br^2 + C where r belongs to [0,L]. I would be grateful if someone could help. I am a beginner in PDEs.

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November 9, 2016, 17:07		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	what is the problem you get?

November 9, 2016, 17:09		#3
debanik1 New Member Choose one... Join Date: Oct 2012 Posts: 8 Rep Power: 13	I am getting oscillations at the start of my domain. I would say spurious values. The equation represents the time evolution of droplet height with radius.

November 9, 2016, 17:39		#5
debanik1 New Member Choose one... Join Date: Oct 2012 Posts: 8 Rep Power: 13	Here is the link to the paper. https://www.cambridge.org/core/journ...1EA3FB2662BBC5 Please refer to (3.1) and (3.2). In case you don't have access to journals, please mention your email id so that I can forward you the paper?