Abstract
We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with a non-divergence-free velocity field. Numerical simulations for advection-dominated problems demonstrate the accuracy and efficiency of the adaptive algorithm for resolving the sharp layers occurring in interface problems with small surface tension.
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Acknowledgements
This work has been partially supported METU Research Fund Project BAP-07-05-2013-004 and by Scientific Human Resources Development Program (ÖYP) of the Turkish Higher Education Council (YÖK).
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Uzunca, M., Karasözen, B., Sarıaydın-Filibelioğlu, A. (2016). Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_18
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DOI: https://doi.org/10.1007/978-3-319-39929-4_18
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