Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations

Email: na.asmith2{at}na-net.ornl.gov Email: na.silvester{at}na-net.ornl.gov The issue of appropriate time discretization methods for theunsteady incompressible Navier-Stokes equations is consideredfrom a practical perspective. Conventional implicit time-steppingalgorithms are not feasible for long-time simulations sincethey inherit the quadratic nonlinearity of the steady-stateequations. As a result, two new linearized versions of the ‘pure’algorithms are analyzed herein. These have similar stabilityproperties and comparable accuracy to the underlying nonlinearmethods.