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Strong vs. weak formulation of the Laplace equation |
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July 3, 2024, 03:26 |
Strong vs. weak formulation of the Laplace equation
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#1 |
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Lars
Join Date: Jul 2024
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Hello everyone,
I am fairly new to OpenFOAM and I have the following question: The weak formulation of the laplace equation reads: \integral_{\Omega} \phi * \laplace T d\Omega = - \integral_{\Omega} \grad{\phi} \grad{T} d\Omega, assuming, that the testfunctions \phi are 0 on the boundary \partial \Omega. But if i implement this in OpenFOAM like the following: fvc::domainIntegrate(\phi * fvc::laplacian(T)).value() and fvc::domainIntegrate(fvc::grad(\phi) & fvc::grad(T)).value(). I obtain different values, but they should be the same in theory. I already searched the internet. Thanks already in advance |
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July 12, 2024, 08:35 |
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#2 |
Senior Member
Join Date: Apr 2020
Location: UK
Posts: 742
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Presumably the answers are close, in which case what you have just demonstrated is that finite volume discretisation is not exact (2nd order at best), and so involves round-off errors.
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