[soufiane002]

hello
could we use the Thomas algorithm (TDMA) to solve a tridimensional problem
thank you

[LuckyTran]

TDMA is generally limited to 2D problems, and very simple ones. Very simple 3D problems usually give block-tridiagonal matrices. But the idea of a simplified Gaussian elimination also exists for block-tridiagonal systems. You could also apply operator splitting techniques that yield multiple tridiagonal systems that could be solved sequentially using TDMA. The bigger issue is that it's easy to violate the "tri" part with higher order discretization schemes and/or unstructured grids. TDMA is good for academic learning but for general purpose 3D CFD, you'll be using some kind of sparse solver.

[Continuum]

Originally Posted by soufiane002

hello
could we use the Thomas algorithm (TDMA) to solve a tridimensional problem
thank you

Yes. You can apply an alternating direction implicit (ADI) formation to create a series of 1D problems, each of which can be solved to the Thomas algorithm. It does require a structured mesh though.