Mass conservation on regular grids for incompressible flow
Abstract
Finitedifference representations of the continuity equation and pressure gradient are investigated for incompressible flow. In the onedimensional case, central differencing necessarily leads to oscillation on regular grids. Oscillation is avoided when pressure and velocity points are staggered, and also when onesided difference approximations are taken in opposite directions for spatial derivatives of velocity and pressure. These findings are employed for solution of the twodimensional NavierStokes equations. Comparison calculations for the flow about a cylinder are made, using three different representations for the pressure gradient and continuity equation: (1) central differencing on a regular grid, (2) onesided differencing on a regular grid, and (3) linewise staggering of pressure and velocity points. Central differencing is used for advective terms in all cases. Without the addition of artificial viscosity, only scheme (3) is stable at high Reynolds number.
 Publication:

17th Fluid Dynamics, Plasma Dynamics, and Lasers Conference
 Pub Date:
 June 1984
 Bibcode:
 1984fdpd.confR....B
 Keywords:

 Computational Fluid Dynamics;
 Cylindrical Bodies;
 Finite Difference Theory;
 Incompressible Flow;
 Two Dimensional Flow;
 Advection;
 Cartesian Coordinates;
 Computational Grids;
 High Reynolds Number;
 Jacobi Matrix Method;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer