Time-Space Adaptive Method of Time Layers for the AdvectiveAllen-Cahn Equation

Karasözen, Bülent
Uzunca, Murat


Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation
UZUNCA, MURAT; Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse (2015-09-18)
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 nondivergence-free velocity fields. Numerical simulations for convection dominated problems demonstrate the accuracy and efficiency of the adaptive algorithm for resolving the sharp layers occurring in interface problems with small surface tension.
Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations
Demir, Medine; Çıbık, Aytekin; Kaya Merdan, Songül (2022-12-15)
© 2022 Elsevier Inc.This paper considers the backward Euler based linear time filtering method for the developed energy-momentum-angular momentum conserving (EMAC) formulation of the time dependent-incompressible Navier-Stokes equations in the case of weakly enforced divergence constraint. The method adds time filtering as a post-processing step to the EMAC formulation to enhance the accuracy and to improve the approximate solutions. We show that in comparison with the Backward-Euler based EMAC formulation ...
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In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multiaffine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition sys...
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Time-domain mapping of electromagnetic ray movement inside anisotropic spherical resonator
Biber, A; Golick, A; Tomak, Mehmet (2002-09-01)
This paper presents the analytical proof of "Time-Domain Mapping Method" for the spherical resonator made up of uniaxial crystal. In this way, the main types of caustics inside the spherical resonator made up of uniaxial crystal, which were investigated numerically before, are confirmed analytically. It is engraved that the problem of the ray flow inside the spherical resonator can be reduced to the problem of the ray flow inside metal cavity shaped as spheroid.
Citation Formats
B. Karasözen and M. Uzunca, Time-Space Adaptive Method of Time Layers for the AdvectiveAllen-Cahn Equation. 2016, p. 184.