{"title":"A Finite Difference Calculation Procedure for the Navier-Stokes Equations on a Staggered Curvilinear Grid","authors":"R. M. Barron, B. Zogheib","volume":47,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1443,"pagesEnd":1447,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5455","abstract":"A new numerical method for solving the twodimensional,\nsteady, incompressible, viscous flow equations on a\nCurvilinear staggered grid is presented in this paper. The proposed\nmethodology is finite difference based, but essentially takes\nadvantage of the best features of two well-established numerical\nformulations, the finite difference and finite volume methods. Some\nweaknesses of the finite difference approach are removed by\nexploiting the strengths of the finite volume method. In particular,\nthe issue of velocity-pressure coupling is dealt with in the proposed\nfinite difference formulation by developing a pressure correction\nequation in a manner similar to the SIMPLE approach commonly\nused in finite volume formulations. However, since this is purely a\nfinite difference formulation, numerical approximation of fluxes is\nnot required. Results obtained from the present method are based on\nthe first-order upwind scheme for the convective terms, but the\nmethodology can easily be modified to accommodate higher order\ndifferencing schemes.","references":"[1] T. F. Miller and F. W. Schmidt, \"Use of a pressure-weighted\ninterpolation method for the solution of the incompressible Navier-\nStokes equations on a non-staggered grid system,\" Numerical Heat\nTransfer , vol. 14, pp. 213-233, 1988.\n[2] G. D. 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