Numerical Framework for Pattern-Forming Models on Evolving-in-Time Surfaces

Authors

  • Ramzan Ali* Technische Universität Dortmund Fakultät für Mathematik Lehrstuhl LSIII Vogelpothsweg 87 44227 Dortmund
  • Andriy Sokolov Institut fur Angewandte Mathematik, TU Dortmund
  • Robert Strehl Institut fur Angewandte Mathematik, TU Dortmund
  • Stefan Turek Institut fur Angewandte Mathematik, TU Dortmund

DOI:

https://doi.org/10.11145/452

Abstract

In this contribution we describe a numerical framework for a system of coupledreaction-diffusion equations В on an evolving-in-time hypersurface$\Gamma$. Numerical tests are empolyed for Turing-type instability on stationary and evolving surfaces.В The proposed framework combines the level set methodology forthe implicit description of the time dependent Р“ , the Eulerianfinite element formulation for the numerical treatment of partialdifferential equations, and the flux-corrected transport scheme for thenumerical stabilization of arising adjective, resp., convective terms.Major advantages of this scheme are that it avoids numerical calculation ofcurvature, allows coupling of surface-defined partialdifferential equations with domain-defined partialdifferential equations through the level set bulk and preserves the positivity of the solution throughthe algebraic flux correction. Corresponding numerical tests demonstratethe ability of the scheme to deliver В highly accurate solutions with a reasonably good convergence behavior.

Author Biography

Ramzan Ali*, Technische Universität Dortmund Fakultät für Mathematik Lehrstuhl LSIII Vogelpothsweg 87 44227 Dortmund

Research Associate

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Published

2015-04-21

Issue

Vol. 2 No. 1 (2015)

Section

Conference Contributions

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