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Semidiscrete formulations for transient transport at small time steps
Author(s) -
Harari Isaac,
Hauke Guillermo
Publication year - 2007
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.1487
Subject(s) - discretization , spurious relationship , advection , temporal discretization , transient (computer programming) , reaction–diffusion system , instability , mathematics , diffusion , galerkin method , mathematical analysis , mechanics , computer science , physics , finite element method , thermodynamics , statistics , operating system
Solutions of direct time‐integration schemes for transient advection–diffusion–reaction problems that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations. This degradation is not an artifact of the time‐marching scheme, but rather a property of the solution of the semidiscrete Galerkin approximation itself. An analogy to steady advection–diffusion–reaction problems with a modified reaction coefficient by the Rothe method of discretizing in time prior to spatial discretization provides an upper bound on the time step for the onset of spatial instability. Spatial stabilization removes this pathology, leading to stabilized implicit time‐integration schemes that are free of spurious oscillations at small time steps. Copyright © 2007 John Wiley & Sons, Ltd.