Lately, I was reading some seminal papers on Fractional Step Algorithms and I found this one:

  • Kim, D., Choi, H. A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids. Journal of Computational Physics, Volume 162, Issue 2, pp. 411-428 (2000)

And I am confused on as to how to use/define the boundary conditions for the auxiliary variables in the method proposed. Specifically, in this paper the use of a second auxiliary velocity is proposed, $\hat{u_i}$, and a certain boundary condition is proposed for it in equation (19). Anyway, the proposed integration method described by equations (12)-(15) seem not to require $\hat{u_i}$ on the boundaries; the rotational part of the momentum equation, equation (12), is solved for $\delta \hat{u}$ which, I think, it can be extrapolated from the cell-center to the faces (in specific, the boundary faces); and equation (13) only requires the surface integration of the left-hand side which only involves the pressure. My question is: Is the latter assertion (the extrapolation of $\delta \hat{u}$) correct? If not, How can I couple the boundary condition $\hat{u_i} = u_i^{n+1}+O(\Delta t^2)$ with equation (12) and equation (14)? How can be implemented?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.