[fv214]

I was wondering For the three-dimensional incompressible NavierStokes
equations with heat transfer, what is the size of each block in the block tridiagonal matrix that arises from a line-implicit, central difference method?

and also For the two-dimensional compressible Euler equations,
what is the size of each block in the block tridiagonal matrix that arises from a
line-implicit, central difference method?


I have done Implicit method for a 1D heat equation before, but right now I'm really puzzled about the mentioned equations and their corresponding block size in the tridiagnal matrix.

Thanks alot

[FMDenaro]

Originally Posted by fv214

I was wondering For the three-dimensional incompressible NavierStokes
equations with heat transfer, what is the size of each block in the block tridiagonal matrix that arises from a line-implicit, central difference method?

and also For the two-dimensional compressible Euler equations,
what is the size of each block in the block tridiagonal matrix that arises from a
line-implicit, central difference method?


I have done Implicit method for a 1D heat equation before, but right now I'm really puzzled about the mentioned equations and their corresponding block size in the tridiagnal matrix.

Thanks alot

For incompressible flows there are linear systems for the momentum as well as for the pressure equations. What are you considering? What about the accuracy order of the central discretization? For a general second order discretization of the second derivative, you see 7 non zero diagonals that can be organized in block tri-diagonal matrix