Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation

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UZUNCA M., KARASÖZEN B., Sariaydin-Filibelioglu A.

European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, Turkey, 14 - 18 September 2015, vol.112, pp.175-183, (Full Text)

• Publication Type: Conference Paper / Full Text
• Volume: 112
• Doi Number: 10.1007/978-3-319-39929-4_18
• City: Ankara
• Country: Turkey
• Page Numbers: pp.175-183
• Open Archive Collection: AVESIS Open Access Collection
• Middle East Technical University Affiliated: Yes

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.