This software project consists of numerical modules meant to compiled into libs:

• monores_grid_t (folder monores) to provide a regular grid
• multires_grid_t (folder multires) to provide a multi resolution grid to perform multi resolution analysis
• an abstract class grid_t to define a common interface for both resolution modules
• a theory helper theory_t to setup initial conditions and allow error analysis

Furthermore there are some modules which are meant to actually run the code:

• rawRunner compiles against monores or multires and performs computation. Output is written to files.
• guiRunner compiles against both resolution modules and provides a live plot to see what's actually going on.
• compaRunner compiles against both resolution modules and performs numerical error analysis to compare the error propagation.

Additionally there are some global header files:

• settings.h holds some default configuration data
• functions.h holds different functions to initialize the computation
• point.hpp defines the attributes of one grid point

This project uses the tools provided by the Qt project for developing and building the source, namely the Qt Creator and QMake.

Although this project takes advantage of Qt tools, Qt itself is only a dependency for the guiRunner module.

The project has been tested with both CLang and GCC compilers. The Makefiles are generated by executing qmake ../path/to/source in the build directory.

• gcc (SUSE Linux) 4.8.1 20130909 [gcc-4_8-branch revision 202388]
• clang version 3.3 (branches/release_33 183898)
• clang version 3.4 (https://github.com/clang-omp/clang 47c90595adcc31d595aabd4db09894b23cbaafd2) openmp-enabled
• QMake version 2.01a

The configuration is done by editing the header files settings.h and functions.h, and as well by providing some defines to the C precompiler.

• define REGULAR to make rawRunner build against the regular grid instead of the multi resolution grid

• define OPENMP to activate openmp, e.g. OPENMP=iomp5or OPENMP=gomp` (You might need to add something like

  LIBS+=-L/usr/local/lib64 OPENMP=iomp5 QMAKE_CXX=/usr/local/bin/clang++ QMAKE_LINK=/usr/local/bin/clang++
  

  to the qmake configuration/call.)

• define LIMITER can be set to enable the limiter for derivatives in the flow calculation

The documentation is generated from the source using Doxygen. Navigate to the repository root directory and run: doxygen doc/Doxyfile

To give an idea of how the program is supposed to work, let's go into details what happens if you run rawRunner compiled against the multiresolution module.

1. Initialization: call the constructor of multires_grid_t
2. set multires_grid_t::m_level_min and multires_grid_t::m_level_max and calculate multires_grid_t::m_level_start and multires_grid_t::dt
3. assign a global (static) node_t::c_epsilon thresholding value to all nodes grid
4. create a root point multires_grid_t::m_root_point and a root node multires_grid_t::m_root_node
5. recursively create new node_t (with dedicated point_t) using node_t::branch() until we reached multires_grid_t::m_level_start
6. optimization of the initial grid starts: loop with initialization of all point_t and multires_grid_t::remesh() (includes creation of savety zone) until the number of points in the grid is stable
7. as long as the grid_t::getTime() did not advance until a given time, multires_grid_t::timeStep() is executed (see below)
8. Finalization: interpolate all points to the finest grid using multires_grid_t::unfold() to ease data output, comparision, etc.

What happens in a multires_grid_t::timeStep() highly depends on the underlying algorithm to do advance in time. In this very simple example, we use a finite volume method (FVM) based direction-splitting scheme. So we first update the flow using node_t::updateFlow() on the intersection to a temporary variable point_t::m_flow. In the next step we use this value to update the field property point_t::m_phi using node_t::timeStep(). Both functions have in common that they recursively walk through the tree and only touch the values of node_t::m_point of nodes that node_t::isLeaf(). After all point_t have been altered accordingly, the geometry of the grid will be adapted using multires_grid_t::remesh(). Finally the internal grid_t::m_time is increased.

1. update recursively all point_t; the step might include multiple tree traversals to respect data dependencies between the point_t
2. multires_grid_t::remesh()
3. node_t::remesh_analyse() sets recursively the active status (node_t::flag_t) to all nodes
4. node_t::remesh_savety() will assure that all active nodes have children with status savety zone
5. node_t::remesh_clean() will delete all nodes that do not have an active or savety zone status; the status of all nodes will be reset at the same time
6. increase grid_t::m_time