Next Article in Journal
Solid-State Testing of a Van-Der-Waals-Corrected Exchange-Correlation Functional Based on the Semiclassical Atom Theory
Previous Article in Journal
Optimization of Airfoils Using the Adjoint Approach and the Influence of Adjoint Turbulent Viscosity
Article Menu

Export Article

Open AccessArticle
Computation 2018, 6(1), 6;

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

Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
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)
Full-Text   |   PDF [1367 KB, uploaded 24 January 2018]   |  


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

Figure 1

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).

Share & Cite This Article

MDPI and ACS Style

Martin, T.; Shevchuk, I. Implementation and Validation of Semi-Implicit WENO Schemes Using OpenFOAM®. Computation 2018, 6, 6.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Computation EISSN 2079-3197 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top