Implementation of A Least Squares Method To A Navier-Stokes Solver

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares solver to the lid driven cavity problem and discuss results

Simulating Dislocation Densities with Finite Element Analysis

A one-dimensional set of nonlinear time-dependent partial differential equations developed by Acharya (2010) is studied to observe how differing levels of applied strain affect dislocation walls. The framework of this model consists of a convective and diffusive term which is used to develop a linear system of equations to test two methods of the finite element method. The linear system of partial differential equations is used to determine whether the standard or Discontinuous Galerkin method will be used. The Discontinuous Galerkin method is implemented to discretize the continuum model and the results of simulations involving zero and non-zero applied strain are computed. The evolution in time of functions for plastic deformation, dislocation density, and internal shear stress are plotted and discussed

A One-dimensional Field Dislocation Mechanics Model Using Discontinuous Galerkin Method

A numerical solution strategy for a one-dimensional field dislocation mechanics (FDM) model using the Discontinuous Galerkin (DG) method is developed. The FDM model is capable of simulating the dynamics of discrete, nonsingular dislocations using a partial differential equation involving a conservation law for the Burgers vector content with constitutive input for nucleation and velocity. Modeling of individual dislocation lines with an equilibrium compact core structure in the context of this continuum elastoplastic framework requires a non-convex stored energy density. Permanent deformation and stress redistribution caused by the dissipative transport of dislocations is modeled using thermodynamics-based constitutive laws. A DG method is employed to discretize the evolution equation of dislocation density yielding high orders of accuracy when the solution is smooth. The trade-offs of using a high order explicit Runge-Kutta time stepping and an implicit-explicit scheme are discussed. The developed numerical scheme is used to simulate the transport of a single screw dislocation wall in the case of a non-zero applied strain

The Materials Experiment Knowledge Graph

Materials knowledge is inherently hierarchical. While high-level descriptors such as composition and structure are valuable for contextualizing materials data, the data must ultimately be considered in the context of its low-level acquisition details. Graph databases offer an opportunity to represent hierarchical relationships among data, organizing semantic relationships into a knowledge graph. Herein, we establish a knowledge graph of materials experiments whose construction encodes the complete provenance of each material sample and its associated experimental data and metadata. Additional relationships among materials and experiments further encode knowledge and facilitate data exploration. We illustrate the Materials Experiment Knowledge Graph (MEKG) using several use cases, demonstrating the value of modern graph databases for the enterprise of data-driven materials science