Finite Difference Approach to Navier-Stokes Equations

Two fluid scenarios are presented below using a two-dimensional direct numerical simulation (DNS) Navier-Stokes solver. This program utilized first-order explicit forward Euler time stepping and second-order differences in space. Various checks to ensure numeric stability and mass conservation are utilized to confirm real world scenarios.

The first scenario is a lid-driven cavity flow with unit sheer velocity at the free surface. Dirichlet boundaries at the walls and cavity floor are set to zero ensure solid boundary behavior. The eddy behavior in the bottom right corner is consistent with various published research in similar lid driven flows.

The second scenario is a jet into an open fluid system. Periodic boundaries are set in the y-direction and a Nuemann zero-gradient boundary condition is set at the far x boundary.