The Reduced Basis Method for Incompressible Viscous Flow Calculations

The reduced basis method is a type of reduction method that can be used to solve large systems of nonlinear equations involving a parameter. In this work, the method is used in conjunction with a standard continuation technique to approximate the solution curve for the nonlinear equations resulting from discretizing the Navier–Stokes equations by finite–element methods. This paper demonstrates that the reduced basis method can be implemented to approximate efficiently solutions to incompressible viscous flows. Choices of basis vectors, issues concerning the implementation of the method, and numerical calculations are discussed. Two fluid flow calculations are considered, the driven cavity problem and flow over a forward facing step.