# CFL condition heat equation 2D/3D

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 November 24, 2011, 11:43 CFL condition heat equation 2D/3D #1 New Member   Join Date: Aug 2009 Posts: 3 Rep Power: 10 I am solving the heat equation in a non comercial C++ finite elements code with explicit euler stepping, and gmesh adaptive meshes (coarse in the boundaries and finer in the center). I am aware the CFL condition for the heat equation depends on dt/h**2 for the 1D, 2D, 3D case. When I solve the equation in 2D this principle is followed and I require smaller grids following dt

 February 4, 2012, 05:54 #2 New Member   Join Date: Aug 2009 Posts: 3 Rep Power: 10 Finally, the issue was merely a meshing problem. I am using gmsh, which allows to provide a 1d parameter of "typical length". Although this parameter is well conserved in 2d meshes, 3d meshes seem to result with very deformed elements (e.g. tetrahedron with one of the edges near to zero). Optimizing the mesh with the two 'optimize' buttons in Gmsh, helped tough, but still some of the tetrahedrons where very small. To corroborate, I solved the same equations in a regular 3D grid, where I was sure the element size was conserved, and indeed, the dt

 February 4, 2012, 08:51 #3 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,503 Rep Power: 40 you can easily check the stability constraint for the parabolic equation Ut = k (Uxx + Uyy +Uzz) using FTCS FD-based scheme, you will see that the constraint involves simultaneously the three mesh steps... Hence the dt must be chosen smaller for multidimensional flows. However, for FEM the stability constraint can be different depending on the shape functions

 Tags cfl, dimension, fem, stability

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