A Second-Order Projection Method for Incompressibl

Ivan

Hi:

I am currently attempting to construct a numerical model utilizing "A Second-Order Projection Method for Incompressible Navier-Stokes Equations" by Bell, Colella, and Glaz. I am experiencing a difficulty with the projection portion of my algorithm and I would like to know if anyone experienced a similar problem during the development of the simulator.

The core component of the numerical method is the orthogonal projection that employs a discrete-Galerkin finite difference formulation to decompose the sum of diffusion-convection terms in Navier-Stokes equations into a divergence free component (dUdt) and the gradient free component (pressure gradient). I am currently experiencing difficulty with my projection algorithm in a sense that the solution that I am obtaining is not unique. In other words, my computed divergence free and gradient free vector fields, generated by decomposition of the diffusion-convection terms associated with two-dimensional Navier-Stokes equations for the uniformly stratified Boussinesque fluid, are numerically divergence and gradient free respectively. Moreover, the dot product of the two is 0 and their sum corresponds to the original diffusion-convection field. However, my numerically obtained solution for this simple test case is different from the exact solution. In that regard, I would like to ask if anyone experienced a similar difficulty while developing projection portion of the simulator by following the algorithm outlined by Bell, Colella, and Glaz.

Thank you very much

Ivan