Finite volume method

Merouaneker · October 13, 2017, 18:07

Hello everybody,
Can you help me to solve the hyperbolic heat conduction equation ?
Actually, I have problem in initial conditions, I don't know how to use it :
T(x,0)=0 and dT(x,0)/dt=0
The equation is :
d²T/dt²+2dT/dt+d²T/dx²=0
Thank you .

Zigec · October 24, 2017, 00:49

You need to integrate your equation two times, with this you will get additional to the final equation two constants (lets call them A and B). After this you use your 2 boundary conditions to solve the yet unknown constants.

After the first integration you get a first order DE in which you insert your second boundary dT() and calculate the first constant.
Then you insert in the final equation (after two interpolations) the now known first constant and your first boundary condition T(). With this you can than calculate your second constant.

The final equation should look something like that:
[equation] + Ax + B

October 13, 2017, 18:07	Finite volume method	#1
Merouaneker New Member Merouane KEROUAZ Join Date: Oct 2017 Posts: 2 Rep Power: 0	Hello everybody, Can you help me to solve the hyperbolic heat conduction equation ? Actually, I have problem in initial conditions, I don't know how to use it : T(x,0)=0 and dT(x,0)/dt=0 The equation is : d²T/dt²+2dT/dt+d²T/dx²=0 Thank you .

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October 24, 2017, 00:49		#2
Zigec New Member Ziga Join Date: Feb 2016 Location: Maribor, Slovenia Posts: 27 Rep Power: 10	You need to integrate your equation two times, with this you will get additional to the final equation two constants (lets call them A and B). After this you use your 2 boundary conditions to solve the yet unknown constants. After the first integration you get a first order DE in which you insert your second boundary dT() and calculate the first constant. Then you insert in the final equation (after two interpolations) the now known first constant and your first boundary condition T(). With this you can than calculate your second constant. The final equation should look something like that: [equation] + Ax + B