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Computation 2018, 6(1), 6; https://doi.org/10.3390/computation6010006

Implementation and Validation of Semi-Implicit WENO Schemes Using OpenFOAM®

1
Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2
Chair of Modeling and Simulation, University of Rostock, 18059 Rostock, Germany
*
Author to whom correspondence should be addressed.
Received: 3 December 2017 / Revised: 15 January 2018 / Accepted: 23 January 2018 / Published: 24 January 2018
(This article belongs to the Section Computational Engineering)
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Abstract

In this article, the development of high-order semi-implicit interpolation schemes for convection terms on unstructured grids is presented. It is based on weighted essentially non-oscillatory (WENO) reconstructions which can be applied to the evaluation of any field in finite volumes using its known cell-averaged values. Here, the algorithm handles convex cells in arbitrary three-dimensional meshes. The implementation is parallelized using the Message Passing Interface. All schemes are embedded in the code structure of OpenFOAM® resulting in the access to a huge open-source community and the applicability to high-level programming. Several verification cases and applications of the scalar advection equation and the incompressible Navier-Stokes equations show the improved accuracy of the WENO approach due to a mapping of the stencil to a reference space without scaling effects. An efficiency analysis indicates an increased computational effort of high-order schemes in comparison to available high-resolution methods. However, the reconstruction time can be efficiently decreased when more processors are used. View Full-Text
Keywords: CFD; high-order methods; WENO reconstruction; semi-implicit; unstructured grids CFD; high-order methods; WENO reconstruction; semi-implicit; unstructured grids
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Martin, T.; Shevchuk, I. Implementation and Validation of Semi-Implicit WENO Schemes Using OpenFOAM®. Computation 2018, 6, 6.

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