A Finite Element Approach to Solve Incompressible Navier-Stokes Equations and Its Convergence Rate Analysis

Finite element methods for fluid flow problems are gaining more interests in nuclear engineering fields in recent years. Based on linear triangle elements, this work implements the algebraic subgrid scale (ASGS) stabilized finite element model for solving advection dominated incompressible fluid flows. The non-linearity is handled by the fixed point iteration. Verification is carried out using the method of manufactured solutions (MMS) for convergence rate analysis and the unit square lid-driven cavity benchmark problem.