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Exponential time integration using Krylov subspaces
Author(s) -
Schulze J. C.,
Schmid P. J.,
Sesterhenn J. L.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1902
Subject(s) - exponential function , truncation (statistics) , mach number , mathematics , truncation error , integrator , computer science , compressibility , krylov subspace , scale (ratio) , range (aeronautics) , computational fluid dynamics , exponential integrator , linear subspace , mathematical optimization , mathematical analysis , mechanics , iterative method , physics , aerospace engineering , differential equation , geometry , engineering , differential algebraic equation , computer network , ordinary differential equation , bandwidth (computing) , quantum mechanics , machine learning
The application of exponential integrators based on Krylov techniques to large‐scale simulations of complex fluid flows with multiple time‐scales demonstrates the efficiency of these schemes in reducing the associated time‐step restrictions due to numerical stiffness. Savings of approximately 50% can be achieved for simulations of the three‐dimensional compressible Navier–Stokes equations while still maintaining a truncation error typical of explicit time‐stepping schemes. Exponential time integration techniques of this type are particularly advantageous for fluid flows with a wide range of temporal scales such as low‐Mach number, reactive or acoustically dominated flows. Copyright © 2008 John Wiley & Sons, Ltd.