An adaptive hp-version of the finite element method applied to flame propagation problems
✍ Scribed by V. China Venkata Rao; P. C. Das; T. Sundararajan
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 409 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
This paper describes an adaptive hp-version mesh reÿnement strategy and its application to the ÿnite element solution of one-dimensional ame propagation problems. The aim is to control the spatial and time discretization errors below a prescribed error tolerance at all time levels. In the algorithm, the optimal time step is ÿrst determined in an adaptive manner by considering the variation of the computable error in the reaction zone. Later, the method uses a p-version reÿnement till the computable a posteriori error is brought down below the tolerance. During the p-version, if the maximum allowable degree of approximation is reached in some elements of the mesh without satisfying the global error tolerance criterion, then conversion from pto h-version is performed. In the conversion procedure, a gradient based non-uniform h-version reÿnement has been introduced in the elements of higher degree approximation. In this way, p-version and h-version approaches are used alternately till the a posteriori error criteria are satisÿed. The mesh reÿnement is based on the element error indicators, according to a statistical error equi-distribution procedure. Numerical simulations have been carried out for a linear parabolic problem and premixed ame propagation in one-space dimension.