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My code...

Ali_Abdul 5
May 23 2020
0 0

@Mariusz Iwaniuk Thank you so much for your quick response. Attached is the code. 
 

``

k := 8.0; Res := 125.0; lambda := 20.0

Omega := 2*lambda/Res

``

L := diff(eta(r, t), r, r)-(diff(eta(r, t), r))/r-k^2

``

L2 := diff(eta(r, t), r, r, r, r)-2*(diff(eta(r, t), r, r, r))/r+3*(diff(eta(r, t), r, r))/r^2-2*k^2*(diff(eta(r, t), r, r))-3*(diff(eta(r, t), r))/r^3+2*k^2*(diff(eta(r, t), r))/r+k^4

``

U := Re((1-BesselJ(0, sqrt(-2*I)*lambda*r)/BesselJ(0, sqrt(-2*I)*lambda))*exp(I*Omega*t)/(I)) 

``plot3d(U, r = 0 .. 1)

 

 

PDE := [diff(L, t)+I*k*(U*eta(r, t)*L+((diff(U, r))/r-(diff(U, r, r)))*eta(r, t))-L2/(lambda*Res)]

``

IBC := [eta(r, 0) = .25*(1-cos(2*Pi*r))+I*.25, eta(0, t) = 0, eta(1, t) = 0, (D[1](eta))(0, t) = 0, (D[1](eta))(1, t) = 0]

sol := pdsolve(PDE, IBC, numeric)

_m140471563071744

 (1)

p1 := sol:-plot(eta(r, t), t = 0, numpoints = 100, r = 0 .. 1, color = ["Blue"], legend = ["η(r,t)"])

p2 := sol:-plot(eta(r, t), t = .5, numpoints = 100, r = 0 .. 1, color = ["Green"], legend = ["η(r,t)"])

 

 

plots:-display({p1, p2})

 

 

````

sol:-plot3d(eta(r, t), t = 0 .. 1, r = 0 .. 1, grid = [100, 100])

 

 

``


 

Download LDNS.mw

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