2007
DOI: 10.1002/fld.1654
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Implicit FEM‐FCT algorithms and discrete Newton methods for transient convection problems

Abstract: SUMMARYA new generalization of the flux-corrected transport (FCT) methodology to implicit finite element discretizations is proposed. The underlying high-order scheme is supposed to be unconditionally stable and produce time-accurate solutions to evolutionary convection problems. Its nonoscillatory low-order counterpart is constructed by means of mass lumping followed by elimination of negative off-diagonal entries from the discrete transport operator. The raw antidiffusive fluxes, which represent the differen… Show more

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Cited by 17 publications
(19 citation statements)
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“…This concept can also be extended [16] to flux limiters which are designed for the treatment of transient flows, e.g. the semi-implicit FEM-FCT limiter proposed in [10].…”
Section: Discussionmentioning
confidence: 99%
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“…This concept can also be extended [16] to flux limiters which are designed for the treatment of transient flows, e.g. the semi-implicit FEM-FCT limiter proposed in [10].…”
Section: Discussionmentioning
confidence: 99%
“…As a consequence, the converged steady-state solution to problem (16) can be computed very efficiently if → ∞ for n → ∞ without loss of accuracy. It is noteworthy that the implicit Euler method (16) leads to algebraic equations which are very similar to those resulting from the use of under-relaxation applied to steady-state flow problems [20, pp. 148-149].…”
Section: Nonlinear Solution Strategiesmentioning
confidence: 99%
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“…Several implicit FEM-FCT schemes were published by the author and his coworkers [16,18,19,26]. The rationale for the use of an implicit time discretization stems from the fact that the CFL stability condition becomes prohibitively restrictive in the case of strongly nonuniform velocity fields and/or locally refined meshes.…”
Section: Introductionmentioning
confidence: 99%
“…Sometimes, too many flux/defect correction cycles are required to obtain a converged solution, especially if the Courant number is large and the contribution of the consistent mass matrix cannot be neglected. The use of a discrete Newton method [26] makes it possible to accelerate convergence but the computational cost per time step is still rather high as compared to that of a fully explicit algorithm. This is unacceptable since the time step for FCT must be relatively small for accuracy reasons.…”
Section: Introductionmentioning
confidence: 99%