A Hierarchical Grid Solver for Simulation of Flows of Complex Fluids.

Tree-based grids bring the advantage of using fast Cartesian discretizations, such as finite differences, and the flexibility and accuracy of local mesh refinement. The main challenge is how to adapt the discretization stencil near the interfaces between grid elements of different sizes, which is usually solved by local high-order geometrical interpolations. Most methods usually avoid this by limiting the mesh configuration (usually to graded quadtree/octree grids), reducing the number of cases to be treated locally. In this work, we employ a moving least squares meshless interpolation technique, allowing for more complex mesh configurations, still keeping the overall order of accuracy. This technique was implemented in the HiG-Flow code to simulate Newtonian, generalized Newtonian and viscoelastic fluids flows. Numerical tests and application to viscoelastic fluid flow simulations were performed to illustrate the flexibility and robustness of this new approach.

Moisture Absorption in Polymer Composites Reinforced with Vegetable Fiber: A Three-Dimensional Investigation via Langmuir Model.

This work aims to study numerically the moisture absorption in polymer composite reinforced with vegetable fibers using the Langmuir model which considers the existence of free and entrapped water molecules inside the material. A three-dimensional and transient modeling for describing the water absorption process inside the composite and its numerical solution via finite volume method were presented and discussed. Application has been made for polymer composites reinforced with sisal fiber. Emphasis was given to the effect of the layer thickness of fluid close to the wall of the composite in the progress of water migration. Results of the free and entrapped solute (water) concentration, local moisture content and average moisture content, at different times of process, and inside the composite were presented and analyzed. It was verified that concentration gradients of the molecules (free and entrapped) are higher in the material surface, at any time of the process, and concentration of free solute is greater than the concentration of entrapped solute. It was verified that the water layer thickness surrounding the composite strongly affects the moisture absorption rate.

Efecto del crecimiento en procesos de reacción difusión, un acercamiento a la biología del crecimiento / Growth effect in diffusion reaction processes, an approach to growth biology

El comportamiento de las ecuaciones de reacción-difusión ha sido estudiado en diversos campos de la biología, la bioingeniería y la química, entre otras. En especial, cuando los parámetros del sistema de reacción-difusión se encuentran en el espacio de Turing, la solución lleva a la formación de patrones de Turing que son estables en el tiempo e inestables en el espacio. Estos patrones pueden modificarse gracias a la acción del crecimiento del dominio donde se desarrolla la reacción. En este artículo se plantea, de forma general, las ecuaciones de reacción-difusión sobre dominios crecientes en 2D y 3D. Además, para estudiar el efecto del crecimiento sobre la formación de patrones se resuelven varios ejemplos numéricos sobre diferentes geometrías. Para la solución numérica se utilizó el método de los elementos finitos en conjunto con el método de Newton-Raphson para la aproximación de las ecuaciones diferenciales parciales no lineales. Se encontró que el crecimiento afecta la formación de patrones de Turing generando estructuras complejas en el dominio

The behavior of reaction-diffusion equations has been studied in different fields of biology, bioengineering and chemistry, among others. Interestingly, when the parameters of reaction-diffusion system are placed in the Turing's space, solution leads to formation of Turing's patterns remaining stable in time and unstable in space. These patterns may be modified due to action of growth of domain where reaction is developed. The objective of present paper is to propose in general, the reaction-diffusion equations over the growing domains in 2D and 3D. Also, to study the growth effect on the patterns formation some numerical examples on different geometries must to be solved. For numerical solution we used the finite elements method together with the Newton-Raphson method to approach of the partial no-linear differential equations. It was noted that the growth to affect the Turing's patterns formation generating complex structures in the domain