Recent developments in computational fluid dynamics based on the Taylor-Galerkin method
The key features of the Taylor-Galerkin (TG) method are illustrated for two classes of problems of significant interest. The first is concerned with the solution of the time-dependent incompressible Navier-Stokes equations. The fluid is assumed to be Newtonian. A time-splitting method is introduced for the numerical time integration of the equations. This consists of three fractional steps dealing respectively with the advective terms, the viscous terms, and the pressure/incompressibility terms. Apart from isolating the necessarily implicit pressure phase, the proposed fractional step method offers the additional advantage of allowing for a separate numerical treatment of the hyperbolic and parabolic parts of the governing equations. In particular, a TG method can be introduced for an accurate treatment of the advection phase. The second class of problems concerns the solution of the unsteady Euler equations for compressible, inviscid gas dynamics. This contains a first order system of conservation laws for mass momentum and energy, which can be written in two Cartesian co-ordinates of a hyperbolic system. Second- order TG-methods for the explicit solution are based on a Taylor series expansion. A two-step version of the TG method can be constructed in a similar fashion to that for the Navier-Stokes equations. The Taylor-Galerkin method is quite easy to formulate and program. It represents a useful tool for the computation of time-accurate solutions to problems in which convection is the dominant transport mechanism.
Bibliographic Reference: Paper presented: Second National Congress on Mechanics, Athens (GR), June 29-30, 1989
Availability: Available from (1) as Paper EN 34614 ORA
Record Number: 198910403 / Last updated on: 1994-12-01
Original language: en
Available languages: en