2-D Unsteady State Heat Conductivity

AI Thread Summary
The discussion focuses on the transition from steady-state to unsteady-state heat conductivity analysis in 2-D using finite element analysis. The user seeks assistance in adapting their existing C++ program, which currently employs a preconditioned conjugate gradient solver for steady-state problems, to incorporate explicit Euler time marching for time-dependent scenarios. They express a need for a lumped capacity matrix and inquire about the relationship between Gaussian quadrature and time-marching algorithms in this context. The thread highlights the challenges faced by those new to engineering concepts while attempting to implement complex algorithms. Overall, the user is looking for guidance on developing a simple unsteady-state algorithm for heat conductivity.
dinaharchery
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Hello all,

I am not an engineer but am trying to learn finite element analysis for solid materials - in particular heat conductivity for time dependent problems in 2-D for a single material. I am interested in the explicit Euler time marching, thus I believe I need a lumped capacity matrix?

I have finished a C++ program using 2-D Steady state heat conductivity, it is very simple (as I said I am not an engineer). Can anyone assist me in translating a 2-D code for steady state heat conductivity to a unsteady state (time dependent) version? Small words please :smile: , I am a computer scientist.

Thanks for any help.
 
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Any idea at all? A simple 2-D unsteady state algorithm?

Thanks again
 
How exactly does your steady-state code compute the solution? Many solvers like this use some sort of pseudo-time, whether you want to call it iterations, or time-steps or whatever.
 
The steady-state code uses a preconditioned conjugate gradient solver, so the solver itself is iterative. I would like to use the explicit euler time marching algorithm but I currently do not have a lumped capacity matrix.
 
I have been doing some research into the unsteady state heat for finite element analysis and have run across Gaussian quadrature. Can anyone explain how this relates to a time-marching algorithm for the FE solution to a simple 2-D (x and y) heat conductivity problem:confused:?

Thanks.
 
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