Viscous incompressible flow simulation using penalty finite element method

Abstract

Numerical analysis of Navier-Stokes equations in velocity- pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flow- widely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.