Dimensional Unstructured Grid Research Articles

Three dimensional simulation of the dynamics of electro active polymers using shell elements

The development of electro active polymers represents a very active branch of research with many applications principally devoted to biological systems. In particular the simulation of these materials is a very important topic in order to predict their behavior. In this work we propose and analyse, from a mathematical point of view, an algorithm for the simulation of active polymers arranged in possibly complex geometries. This algorithm has been designed to be implemented with three dimensional unstructured grids coupled with shell elements to take into account, in a computationally efficient manner, boundary effects and boundary layers. In particular we focus on the existence of a discrete and positive solution of the algorithm. A comparison between the results obtained and the experimental data is included: we aim to reproduce the results obtained by two classical tests in this field i.e. the electric impedance spectroscopy and the displacement of polymers when subjected to an external electric field.

A stabilized element-based finite volume method for poroelastic problems

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier–Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

A process study of the interaction of tidal currents, tidal mixing and density gradients in a region of freshwater influence

Abstract A three dimensional unstructured grid model of the west coast of Britain is used to study the process of the interaction of tidal currents, tidal mixing and density gradient in the Liverpool Bay region. Calculations with M 2 tidal forcing and omitting freshwater discharge show that tidal currents in the region are strong (of order 1 ms − 1 ), with tidal current ellipses essentially rectilinear in the surface and bottom. In the absence of tidal forcing, the freshwater is confined to a thin surface layer. With the inclusion of tidal mixing the surface layer thickens, and in the shallow water area mixed layer occupies the whole water depth. This has a significant effect of reducing its lateral spread. A detailed study of time series of velocity, salinity and turbulence reveals that at flood tide, more saline water is advected into the coastal region and rapid vertical mixing occurs, whereas at ebb tide, fresher water is advected over more saline water. The induced strong pycnocline uncouples surface and bottom layers leading to more circular tidal ellipses which rotate in opposite directions in the vertical, as found in observations. The three dimensional nature of the model reveals that this process involves both horizontal and vertical density gradients, and shows significant horizontal variability in the Liverpool Bay region.

Shock capturing schemes with local mesh adaptation for high speed compressible flows on three dimensional unstructured grids

This paper contributes towards a more complete approach to capture very strong shocks in various applications of high speed compressible Navier–Stokes flows including blasts and explosions using second order finite volume method on unstructured grids. The HLLC Riemann solver is employed to solve for fluxes at cell interfaces with second order approximation of local Riemann states, thus obtaining second order accuracy. In order to stabilize solutions due to high order approximation of solutions in the presence of discontinuities, several strategies are presented in this work. Slope limiters are first explored on unstructured grid to maintain monotonicity of the solution reconstruction following local extremum diminishing (LED) or total variation diminishing (TVD) criteria. The hybrid HLLC/HLLE scheme is appended to eliminate shock instabilities in very strong shock cases. To improve resolution of shocks, a local mesh adaptation scheme is used to increase mesh resolution in areas of high gradients. The scheme only regenerates mesh locally and is proven to be robust and efficient for capturing of unsteady shock propagation applications. Comparisons on the accuracy and performance of different methods on various applications are drawn to suggest a more robust and efficient method for capturing shocks on unstructured grids.

A fully three dimensional unstructured grid non-hydrostatic finite element coastal model

The non-hydrostatic model FINEL3D is based on the finite element method. In the model no approximations to the non-hydrostatic equations have been made. The model uses a 3-D fully unstructured grid and tetrahedral elements. The calculations presented here use the so called mini-element. In this paper the models capability to simulate internal flow and internal wave formation over small scale topography are considered. The flow of a stratified fluid over small scale topographic features in an estuary may generate considerable non-hydrostatic internal wave activity. The model is shown to accurately simulate internal trapped waves and internal lee waves. Differences between the analytical solutions and the model results are shown to be due to numerical diffusion.