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IMA Journal of Numerical Analysis 1997 17(4):527-545; doi:10.1093/imanum/17.4.527
© 1997 by Institute of Mathematics and its Applications
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Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations

ANTONY SMITH{dagger} and DAVID SILVESTER{ddagger}

Mathematics Department, UMIST Manchester M60 1QD, UK

{dagger} Email: na.asmith2{at}na-net.ornl.gov

{ddagger} Email: na.silvester{at}na-net.ornl.gov

The issue of appropriate time discretization methods for the unsteady incompressible Navier-Stokes equations is considered from a practical perspective. Conventional implicit time-stepping algorithms are not feasible for long-time simulations since they inherit the quadratic nonlinearity of the steady-state equations. As a result, two new linearized versions of the ‘pure’ algorithms are analyzed herein. These have similar stability properties and comparable accuracy to the underlying nonlinear methods.


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