Abstract
The NS equations were solved by the use of a CMSSL library subroutine which directly inverts the Poisson matrix. The mathematical approach which sets a scheme for the parallelisation of the Poisson solver subroutine leads to results which are compatible with schemes based on iterative methods used in early calculations such as the Gauss-Seidel. Despite the change of sparsity and size of the Poisson matrix, as the fluid advances in space, one believes that the Bi-conjugate gradient and the Lanczos algorithms are the best candidates for maximum parallelisation of the solver subroutine.
Also, the extension of the problem to 3D is possible because the mathematical approach is still applicable with the VOF technique.
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References
Vinje, T. and Brevig, P.: Adv. Wat. Res. 4 No 2 (1981) 77–82
Grilli, S and Svendsen, I.A.: Water Wave Kinematics. Ed by Tørum, A and Gudmetad, O.T. Kluwer Academic publisher (1989) 387–412
Hirt, C.W. and Nichols, B.D.: J. Comp. Phys. 39/1 (1981) 201–225
Sabeur, Z.A., Roberts, W. and Cooper, A.J.: 4th ICFD Conference on Numerical Method in Computational Fluid Dynamics, Oxford University Press, Edited by Morton, K.W. and Baines, M.J. (1995) (in press)
Ranshaw, J.D. and Trapp, J.A.: J. Comp. Phys. 21 (1976) 438–453
Burden, R.L., Douglas Faires, J. and Reynolds, A.C.: Numerical Analysis (Prindle, Weber and Schmidt, Boston Massachussets) second edition (1981)
CM Fortran: Reference Manual, Thinking Machine Corporation, Cambridge, Massachussets, USA, (1991)
CMSSL Release: Notes for the CM-200, Thinking Machine Corporation, Cambridge, Massachussets, USA, (1993)
Fletcher, H.: Lecture Notes Math. 506 (1976) 73–98 Springer-Verlag
Lanczos, C.: J. Res. Nat. Bur. Stand. 49 (1952) 33–53
Cooker, M.J. and Peregrine, D.H.: 22nd Int. Conf. on Coastal Eng. Netherlands (1990) ASCE
Veldman, A.E.P.: private discussion
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Sabeur, Z.A. (1996). A parallel computation of the Navier-Stokes equation for the simulation of free surface flows with the volume of fluid method. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing Computations in Physics, Chemistry and Engineering Science. PARA 1995. Lecture Notes in Computer Science, vol 1041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60902-4_51
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DOI: https://doi.org/10.1007/3-540-60902-4_51
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