Navier-Stokes Solver using SIMPLE

A MATLAB code to solve the steady and incompressible form Navier-Stokes Equations for a Lid-Driven Cavity

This is a MATLAB code that solves the 2D, steady and incompressible form of the Navier-Stokes Equations using the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE). Meshes for the U and V momentum are staggered whereas the Pressure mesh is the regular control volume formed by a grid generated to discretize the flow domain. The Pressure correction equations are over-relaxed while the velocity solvers are under-relaxed. Velocity corrections are not carried through for the boundary conditions and are terminated by setting the corresponding P coefficient to a large value. Velocity solvers use the upwind interpolation scheme for obtaining velocities at the staggered-cell faces. Mass conservation monitor is displayed every 100 iterations to see the computed mass-imbalance die out as successive iterations follow. Post-processing is done in the same code using quiver function by interpolating U, V velocities from the staggered mesh to the cell corners of the regular mesh. Contour plots are obtained using the contourf function by setting the colormap to 'jet' or 'hsv' .