Preconditioners for hyperbolic systems are numerical artifacts to accelerate the convergence to a steady state. In addition, the preconditioner should also be included in the artificial viscosity or upwinding terms to improve the accuracy of the steady state solution. For time dependent problems we use a dual time stepping approach. The preconditioner affects the convergence rate and the accuracy of the subiterations within each physical time step. We consider two types of local preconditioners: Jacobi and low speed preconditioning. We can express the algorithm in several sets of variables while using only the conservation variables for the flux terms. We compare the effect of these various variable sets on the efficiency and accuracy of the scheme.
@article{M2AN_2005__39_3_515_0,
author = {Turkel, Eli and Vatsa, Veer N.},
title = {Local preconditioners for steady and unsteady flow applications},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {515-535},
doi = {10.1051/m2an:2005021},
mrnumber = {2157148},
zbl = {1130.76055},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_3_515_0}
}
Turkel, Eli; Vatsa, Veer N. Local preconditioners for steady and unsteady flow applications. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 515-535. doi : 10.1051/m2an:2005021. http://gdmltest.u-ga.fr/item/M2AN_2005__39_3_515_0/
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