PF_CaseStudy: Phase Field Simulation Example Code

Case studies from Programming Phase-Field Modeling, but with C++.

Summary

This repository presents the C++ code for the first 5 case studies in book Programming Phase-Field Modeling, by S. Bulent Biner.

This implementation is based on object orientated programming paradigm, with slightly little C++ templates.

Please take the code presented here as an exercise and attempt for exploring the possibility for a generalized phase field program.

Code Overview

There are six folders, with five folders containing case studies from 1 to 5, and a folder named include containing all headers used in each case study.

Case Studies

Below are the details of each case study. Please notice that several case study is not fully implemented as the example in the book.

• CaseStudy_1: A-B alloy spinodal decomposition;

  • Cahn-Hilliard (C-H) equation example;
  • Double well bulk energy;
  • Simple gradient interface energy;

• CaseStudy_2: Grain growth (Partially implemented with only two grains growth);

  • Allen-Cahn (A-C) equation example;
  • Polynomial bulk energy for multiple grain/phase variables: half-double-well energy for single phase variable added with interaction from other phase variables;
  • Simple gradient interface energy;

• CaseStudy_3: Solid state sintering

  • C-H equation for density and A-C equation for phase variable;
  • Double well energy from density;
  • Polynomial energy from phase variable coupled with density;
  • Simple gradient interface energy for both density and phase variable;
  • Complex diffusion, using interpolation function;

• CaseStudy_4: Dendrite growth

  • A-C equation for phase variable;
  • Conservation law of enthalpy for temperature evolution, with simple latent heat contribution;
  • Double well bulk energy for phase variable coupled with supercooling;
  • Gradient interface energy with anisotrophic gradient coefficient;

• CaseStudy_5: Cell motility

  • Soft cell motion;
  • A-C equation coupled with velocity field;
  • Velocity field decomposed into surrounding action part and active part;
  • Complex bulk energy coupled with constant volume restriction;
  • Interface energy describing interaction between cells (part of bulk energy form CaseStudy_2);

Class framework

The code of these five case studies are all based on a set of class and method. Here is a breif introduction to the framework.

Overall Structure

The whole data structure is based on Mesh - MeshNode - EntryNode - Entry model. It means that:

• There should be only one mesh with several points;
• On each point there will be a mesh node;
• In each mesh node, there should be several entry nodes representing different physical properties, such as phase variable, density, concentration.
• In each entry node, there are several entries for different variables.

For example, if there is a simulation of two concentration and one phase variable, with simulation region size of $100\times 100$, then there should be exactly one mesh, 10000 mesh node; in each mesh node there are two active entry node, for concentration and phase variable, and for concentration node, there will be two entry, element 1 and element 2; as for phase variable, there will be only one entry.

File Structure

With such structure design, the file structure is quite direct and simple.

• BaseEntry.hh: All kinds of entry will be here, derived from a parent class BaseEntry defined here.
• BaseNode.hh: All kinds of node defined, also derived from a parent class BaseNode defined here as well.
• MeshNode.hh: A mesh node to manage all base node. Can be considered as a node manager
• PFM.hh: A header for including everything that will be used in each case study.
• PFMTools.hh: A header for several utilities, such as timer or boundary value check, which are less relative to the data structure described before.
• SimulationMesh.hh: A header to define the whole mesh.

And, with such data structure, algorithms related to each structure become a part of method for each class. For instance, the algorithm to calculate laplacian is method of SimulationMesh, while update value of each node will be traced back to the method of BaseNode since all properties should be updated.