# A Fourth-Order Compact Scheme for the Navier-Stokes Equations in irregular domains

## Main Article Content

## Abstract

We present a high-order finite difference scheme for Navier-Stokes equations in irregular domains. The discretization offered here contains two types of interior points. The first is regular interior points, where all eight neighboring points of a grid point are inside the domain and not too close to the boundary. The second is interior points where at least one of the closest eight neighbors is outside the computational domain or too close to the boundary. In the second case we design discrete operators which approximate spatial derivatives of the streamfunction on irregular meshes, using discretizations of pure derivatives in the $x$, $y$ and along the diagonals of the element.

## Article Details

How to Cite

Fishelov, D.
(2016).
A Fourth-Order Compact Scheme for the Navier-Stokes Equations in irregular domains.

*Proceedings Of The Conference Algoritmy,*, 135-144. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/402/319
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Articles

## References

[1] M. Ben-Artzi and I. Chorev and J-P. Croisille and D. Fishelov, A compact difference scheme for the biharmonic equation in planar irregular domains SIAM J. Numer. Anal., 47 (2009), pp. 3087–3108.

[2] M. Ben-Artzi and JP. Croisille and D. Fishelov, A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier–Stokes Equations J. Sci. Comput., 42 (2010), pp. 216–250.

[3] M. Ben-Artzi and J-P. Croisille and D. Fishelov and S. Trachtenberg, A Pure-Compact Scheme for the Streamfunction Formulation of Navier–Stokes equations J. Comput. Phys., 205 (2005), pp. 640–664.

[4] A. Ditkowski and Y. Harness, High-Order Embedded Finite Difference Schemes for Initial Boundary Value Problems on Time Dependent Irregular Domains J. Sci. Comput., 39 (2009), pp. 394–440.

[5] J. W. Stephenson Single cell discretizations of order two and four for biharmonic problems J. Comput. Phys., 55 (20091984), pp. 65–80.

[2] M. Ben-Artzi and JP. Croisille and D. Fishelov, A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier–Stokes Equations J. Sci. Comput., 42 (2010), pp. 216–250.

[3] M. Ben-Artzi and J-P. Croisille and D. Fishelov and S. Trachtenberg, A Pure-Compact Scheme for the Streamfunction Formulation of Navier–Stokes equations J. Comput. Phys., 205 (2005), pp. 640–664.

[4] A. Ditkowski and Y. Harness, High-Order Embedded Finite Difference Schemes for Initial Boundary Value Problems on Time Dependent Irregular Domains J. Sci. Comput., 39 (2009), pp. 394–440.

[5] J. W. Stephenson Single cell discretizations of order two and four for biharmonic problems J. Comput. Phys., 55 (20091984), pp. 65–80.