WENO framework

Weighted essentially non-oscillatory library for the framework of OpenFOAM. Detailed information about the theoretical background and the implementation can be found in:

• J. W. Gärtner, A. Kronenburg, T. Martin, Efficient WENO library for OpenFOAM, SoftwareX, 2020
• T. Martin and I. Shevchuk, Implementation and Validation of Semi-Implicit WENO Schemes Using OpenFOAM, Computation, 2018
• Solving the Level Set Equation using High-order Non-oscillatory Reconstruction

A quick overview of the WENO scheme is provided in this presentation:

• Presentation: WENOExt

Please also check out the Discussion board of GitHub for more information about features or if you want to post a new idea.

Versions:

Major development stages of the library are marked by tags and recently also have a release with a DOI.

Supported OpenFOAM Versions:

• OpenFOAM (ORG) v5.x - 8
• OpenFOAM (ESI) v1912-v2012

Authors

• Tobias Martin [email protected]
• Jan Wilhelm Gärtner [email protected]

When using this work please cite:

J. W. Gärtner, A. Kronenburg, and T. Martin, “SoftwareX Efficient WENO library for OpenFOAM”, SoftwareX, vol. 12, p. 100611, 2020, doi: 10.1016/j.softx.2020.100611.

T. Martin, and I. Shevchuk, “SoftwareX Efficient WENO library for OpenFOAM,” Computation, vol. 6(6), 2018, doi: 10.3390/computation6010006.

Installation

1. Clone the directory with git clone https://github.com/WENO-OF/WENOEXT.git

2. Execute Allwmake to build the library The compilation of the library uses cmake instead of wmake files!

Options

Parallel compilation can be activated with: ./Allwmake -j <# of cores> if the number of cores is omitted then the number of cores is determined automatically.

On the master branch only clean git commits can be compiled. If a dirty git state shall be compiled the -f|--force option has to be used on the master branch.

By default the march=native compiler flag is activated. For some cases it is necessary to deactive this flag. To deactivate this flag use: ./Allwmake -DMARCH_NATIVE=OFF

To compute the eigenvalues of a matrix and the Jacobi inverse matrices own functions defined in mathFunctionsWENO are used. It is possible to switch on the usage of LAPACK libraries by setting ./Allwmake -DUSE_LAPACK=ON If switched on, check with the WENO-PerformanceTests if the performance improves or decreases.

Note to GNU compiler:

GNU compiler version must be higher than 7. For g++ < v7 an error is reported for the specialisation template syntax. The syntax in the code is according to C++11 standard which is available for g++ v7 and higher.

Usage

To use the WENO scheme you have to add the library to your controlDict by editing system/controlDict

libs("libWENOEXT.so")

Within your system/fvSchemes file,

divSchemes
{
    div(phi,U) 	Gauss WENOUpwindFit 2 1;
}

Here the first index '2' represents the order of the WENO scheme and the second index can be either '1' for bounded or '0' for unbounded.

Further options can be set in the WENODict located in the 'system/' folder:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2.3.0                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      WENODict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
// This dict contains expert parameters, which modify the standard WENO scheme.

    //- Stencil extension ratio:
    //  - < 2.5 :   decreased computational effort. May also decrease stability
    //              and accuracy
    //  - > 2.5 :   higher stability. May influence the accuracy of the SVD
    extendRatio     2.5;

    //- WENO stencil weighting parameters:
    p               4.0;
    dm              1000.0;

    //- Calculate best conditioned matrix
    //  This can save memory especially for high order WENO scheme
    //  Increases the calculation time! Default is off
    bestConditioned true;
    
    writeData       true; // Write out the collected stencil list and matrix data
                          // default is 'true' 

    maxCondition    1E-05;// Inverse of the maximum condition that the pseudo 
                          // inverse can have. Only change if you know what you
                          // are doing!

    checkCondition  false;// Check the condition of the pseudo inverse matrix
                          // If the central stencil has at least one zero entry
                          // the matrix is removed for all stencils of this cell.
// ************************************************************************* /

Specialized Version for Scalar Transport

The limited WENOUpwindFit scheme uses a cell limited approach known from other schemes such as linearUpwind. For scalar transport in the range 0 to 1 a specialized scheme called WENOUpwindFit01 is available. This schemes limits the value using the limiter of Zhang and Shu.

Tutorials

The code contains two tutorials from the standard cavity test. To run the tutorials execute ./Allrun in the tutorial/ directory.

Tests

Testing is performed with the CATCH2 framework. You can compile and execute the tests by executing ./runTest in the test directory. Further instructions are found in here

Contineous Integration

To check the code for different OpenFOAM implementations, e.g. OpenFOAM 8, OpenFOAM v1912, etc. the code is copied into different docker containers created with the Dockerfiles in CI/. In the docker container the code is compiled and unit tests executed.

Executing the tests is controlled over the Makefile in the root directory. The different OpenFOAM versions can be tested with

# Just executing make runs all tests
make

# For OpenFOAM v5.x
make runTestsOF5

# For OpenFOAM 8
make runTestsOF8

This implementation allows to have the same testing on the local and remote branch.

License

This OpenFOAM library is under the GNU General Public License. This library contains the Blaze library licensed under the BSD license. Redistribution and use of the Blaze source code with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
• Neither the names of the Blaze development group nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.