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Convergence order of a simple laplacianFoam case

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Old   September 9, 2021, 10:50
Default Convergence order of a simple laplacianFoam case
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David
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Hi everyone,


I'm simulating a simple case using `laplacianFoam` (it's actually a slightly modified version of `laplacianFoam` which takes a non-zero RHS into account, but this should not matter for the overall question) on a two-dimensional rectangular domain. Since initial conditions as well as boundary conditions are space and time dependent, I use `funkySetFields` in order to initialize my domain and `groovyBC` in order to apply the space-time dependent Dirichlet boundary conditions on all domain boundaries.


The test case has a known analytic solution, so that I can evaluate the error at each individual time step. However, I would expect the error convergence to be of second order, whereas I observe only first order convergence.


The relevant settings from my fvSchemes are essentially


Code:
    grad(T)         Gauss linear;

    laplacian(DT,T) Gauss linear corrected;
which are according to the OpenFOAM documentation both second order schemes. Only my time discretization is of first order, but the problem is linear in time, so that I don't expect relevant errors from this side.


Is my expectation of a second order convergence simply wrong or do you see any obvious errors in my simulation setup? Any hints are very welcome.


Thanks in advance and best regards,
David
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