Numerical simulation of two-dimensional flows over a circular ...

A.L.F. Lima E Silva et al. / Journal of Computational Physics 189 (2003) 351–370 355Fig. 2. Scheme for the pressure and velocity interpolation.The different terms described by Eqs. (9)–(12) must be evaluated over the interface using the velocity field~V ð~xÞ and pressure field Pð~xÞ. These calculations must also take into account that, at the interface, the fluidvelocity must be equal to the interface velocity, which guarantees the no-slip condition. The velocity andpressure spatial derivatives are calculated using the fluid velocity and pressure obtained by Eqs. (2) and (3).One of the possible ways to do this is to interpolate ~V ð~xÞ and Pð~xÞ over appropriate points near the interface,as illustrated by Fig. 2. This interpolation method is described in the following section.2.3. Interpolation and derivatives calculation procedureThe interpolation scheme for the horizontal velocity, over point number 3, for example, is shown inFig. 3. A square dotted domain is defined as being the region where the variables will be analyzed. In theFig. 3. Interpolation scheme for the horizontal velocity at point 3.