### Abstract

Based on Poisson equation for pressure, a nodal numerical scheme is developed for the time-dependent, incompressible Navier-Stokes equations. Derivation is based on local transverse-integrations over finite size brick-like cells that transform each partial differential equation to a set of ordinary differential equations (ODEs). Solutions of these ODEs for the transverse-averaged dependent variables are then utilized to develop the difference scheme. The discrete variables are scalar velocities and pressure, averaged over the faces of brick-like cells in the (x,y,t) space. Cell-interior variation of transverse-averaged pressure in each spatial direction is quadratic. Cell-interior variation of transverse-averaged velocity in each spatial direction is a sum of a constant, a linear and an exponential term. Due to the introduction of delayed coefficients, the exponential functions are to be evaluated only once at each time step. The semi-implicit scheme has inherent upwinding. Results of applications to several test problems show that the scheme is very robust and leads to a second-order error. As expected in such coarse-mesh schemes, even relatively large size cells lead to small errors. Extension to three dimensions is straightforward.

Original language | English (US) |
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Pages (from-to) | 168-196 |

Number of pages | 29 |

Journal | Journal of Computational Physics |

Volume | 187 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2003 |

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### Keywords

- Coarse-mesh
- Difference equations
- Inherent upwinding
- Navier-Stokes
- Nodal analytical

### ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics