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A note on the regularization of the discrete Poisson-Neumann problem. (English) Zbl 1034.76043

The time integration of incompressible flow equations leads to a Poisson problem for pressure with Neumann boundary conditions. This problem has a solution only if a compatibility condition is fulfilled. Here the author considers a regularization of the problem, and applies the method to a lid-driven cavity flow.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI

References:

[1] Gresho, P. M.; Sani, R. L., On pressure boundary conditions for the incompressible Navier-Stokes equations, Int. J. Num. Meth. Fluids, 7, 1111 (1987) · Zbl 0644.76025
[2] Gresho, P. M.; Sani, R. L., On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory, Int. J. Numer. Meth. Fluids, 11, 587 (1987)
[3] de Foy, B.; Dawes, W., Unstructured pressure-correction solver based on a consistent discretization of the Poisson equation, Int. J. Numer. Meth. Fluids, 34, 463 (2000) · Zbl 0973.76058
[4] Abdallah, S., Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, I, J. Comp. Phys., 70, 182 (1987) · Zbl 0615.76034
[5] Sotiropoulos, F.; Abdallah, S., The discrete continuity equation in primitive variable solutions of incompressible flow, J. Comput. Phys., 95, 212 (1991) · Zbl 0725.76058
[6] Sotiropoulos, F.; Abdallah, S., A Primitive variable method for the solution of three-dimensional incompressible viscous flow, J. Comput. Phys., 103, 336 (1992) · Zbl 0763.76055
[7] Tafti, D., Alternate formulations for the pressure equation Lplacian in a collocated grid for solving the unsteady incompressible Navier-Stokes equations, J. Comput. Phys., 116, 143 (1995) · Zbl 0817.76048
[8] Briley, R. W., Numerical method for predicting three-dimensional steady viscous flow in ducts, J. Comput. Phys., 14, 8 (1974) · Zbl 0271.76024
[9] Ghia, U.; Ghia, K. N.; Studerus, C. J., A study of Three-Dimensional Laminar Incompressible Flow in Ducts (1976) · Zbl 0364.76017
[10] Ghia, K. N.; Hankey, W. L.; Hodge, J. K., Study of Incompressible Navier-Stokes Equations in Primitive Variables Using Implicit Numerical Technique (1977)
[11] Henshaw, W. D., A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids, J. Comput. Phys., 113, 13 (1977) · Zbl 0808.76059
[12] Pozrikidis, C., Introduction to Theoretical and Computational Fluid Dynamics (1997) · Zbl 0886.76002
[13] C. Pozrikidis, On the relation between the pressure and the projection function for the numerical computation of viscous incompressible flow, submitted for publication.; C. Pozrikidis, On the relation between the pressure and the projection function for the numerical computation of viscous incompressible flow, submitted for publication. · Zbl 1051.76595
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