A Taylor-Galerkin method for the use of finite elements in a nonlinear problem for the numerical modeling of a new Chemo-Fluid oscillator
Main Article Content
Abstract
In this work, a finite element scheme is proposed using a method of Euler-Taylor-Galerkin
described inPáez (2016), for a non-linear model which describes the behavior of a new chemofluidic
oscillator (Donea, 1984). This model is expressed by the coupling of an ordinary
differential equation describing the hydrogel dynamics, the non-linear transport equation and an
auxiliary equation determining the flux volume. The numerical solution is constructed by taking a
semi-discretization in time of the transport equation, employing forward-time Taylor series
expansions including time derivatives of second order and third order, avoiding instabilities
problems. In this semi discrete equation, the spatial variable is approximated by the finite element
formulation according to Galerkin. Some simulations are carried out taking different initial
conditions for the concentration of the hydrogel. The numerical results describe the oscillatory
behavior of the system as in Donea (1984), where MatLab tools are used as black box.
Downloads
Metrics
Article Details
Licensing
TURCOMAT publishes articles under the Creative Commons Attribution 4.0 International License (CC BY 4.0). This licensing allows for any use of the work, provided the original author(s) and source are credited, thereby facilitating the free exchange and use of research for the advancement of knowledge.
Detailed Licensing Terms
Attribution (BY): Users must give appropriate credit, provide a link to the license, and indicate if changes were made. Users may do so in any reasonable manner, but not in any way that suggests the licensor endorses them or their use.
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
