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.
Highlights
In recent years, open source Computational Fluid Dynamics (CFD) codes experienced an increased influence on ongoing science and on the industry
As proposed by Toro [29], we extend Godunov’s first-order version, which is based on cell centre values of Φ±, by higher-order terms of the reconstruction; the so-called WENOUpwindFit arises as a high-order non-oscillatory upwind scheme
If the non-oscillatory behaviour of the scheme is in the first place and the theoretical order of accuracy is less important, a more efficient gradient scheme can be derived by replacing the gradient of Φ by its polynomial representation and evaluating the volume integral with second order of accuracy
Summary
Open source Computational Fluid Dynamics (CFD) codes experienced an increased influence on ongoing science and on the industry. Non-linear schemes were developed such as TVD schemes which are based on limiters derived from corresponding conditions of Sweby [6] Their main drawbacks are the degeneration to first-order accuracy near extrema regardless of a smooth peak or discontinuity and at most second-order accuracy. The possibility to build a semi-implicit finite volume WENO convection scheme arises by including the reconstruction in OpenFOAM® due to existing code structures for such an implementation. It results in a more stable reconstruction for larger time steps and an utilization of high-order convection schemes in common semi-implicit solution algorithms such as SIMPLE or PISO (Pressure-Implicit with Splitting of Operators).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
