Flux-Corrected Transport (FCT) is a conservative, monotone technique for integrating generalized continuity and hydromagnetic equations. It is especially useful for solving compressible-flow problems, particularly those involving shock and rarefaction waves, and contact discontinuities. FCT accomplishes this objective by combining integration schemes with low and high orders of spatial accuracy. The low-order scheme provides a monotone solution, usually by the introduction of diffusive numerical fluxes, while the high-order scheme provides high accuracy in regions of smooth flow and shallow gradients. The high-order solution is obtained by "antidiffusing" the low-order, monotone solution, but only to such an extent that no new extrema are created and no existing extrema are accentuated. This is done by limiting, or "correcting," the antidiffusive fluxes of the high-order scheme, hence the name Flux-Corrected Transport.
FCT was the first of the class of high-order, monotone schemes (FCT is one of many schemes that can be classified TVD) for solving generalized continuity equations (e.g., the equations of Eulerian hydrodynamics). The version of FCT that was used for all of the computations displayed at this site was originally coded by the Laboratory for Computational Physics at the Naval Research Laboratory.
Click on the pictures below to see some typical results that I have obtained for both reactive and non-reactive flow problems.
| Time: | 60 microseconds | 87 microseconds |
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1000 (horizontal) by 720 (vertical) computational cells
| Time: | 60 microseconds | 87 microseconds |
| Regular Grid: |
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| Jiggled Grid: |
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The following results were obtained using a direction split FCT code with single step chemistry and Arrhenius kinetics. The pictures are plots of (from top to bottom) pressure gradient, temperature gradient, vorticity, and gradient of fuel mass fraction. The pictures obtained for overdrive 1.2, activation temperature 10 and heat release parameter 50. They are smoother than other results because in these computations, grid jiggling was used on the 1000 by 500 grid.
The first sequence of pictures are JPEG with size 95k each.
The next pictures show the pressure and temperature fields for one time step. (JPEG, 140k each).
