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[1] Vuorinen, V., Keskinen, J.P., Duwig, C. & Boersma, B., On the implementation of low-dissipative Runge-Kutta projection methods for time dependent flows using Open- FOAM. Computers & Fluids, 93, pp. 153–163, 2014. [Crossref]
[2] Shen, C., Sun, F. & Xia, X., Implementation of density-based solver for all speeds in the framework of OpenFOAM. Computer Physics Communications, 185(10), pp. 2730–2741, 2014. [Crossref]
[3] Sanderse, B. & Koren, B., Accuracy analysis of explicit Runge-Kutta methods applied to the incompressible Navier-Stokes equations. Journal of Computational Physics, 231(8), pp. 3041–3063, 2012. [Crossref]
[4] Kazemi-Kamyab, V., van Zuijlen, A. & Bijl, H., Analysis and application of high order implicit Runge-Kutta schemes to collocated finite volume discretization of the incom- pressible Navier-Stokes equations. Computers and Fluids, 109, pp. 107–115, 2015. [Crossref]
[5] Alexander, R., Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. SIAM Jour- nal on Numerical Analysis, 14, pp. 1006–1021, 1977. [Crossref]
[6] Hairer, E. & Wanner, G., Solving Ordinary Differential Equation II, 2010.
[7] Erturk, E., Corke, T. & Gokcol, C., Numerical solutions of 2-D steady incompress- ible driven cavity flow at high reynolds numbers. International Journal for Numerical Methods in Fluids, 72, pp. 1490–1512, 2007.
[8] Botella, O. & Peyret, R., Benchmark spectral results on the lid-driven cavity flow. Com- puters & Fluids, 27(4), pp. 421–433, 1998. [Crossref]
[9] Inoue, O. & Hatakeyama, N., Sound generation by a two-dimensional circular cylinder in a uniform flow. Journal of Fluid Mechanics, 471, pp. 285–314, 2002. [Crossref]
[10] Muller, B., High order numerical simulation of aeolian tones. Computers & Fluids, 37,
pp. 450–462, 2008. [Crossref]
[11] Isaev, S.A., Baranov, P., Kudrayavtsev, N., Lysenko, D. & Usachev, A., Comparative analysis of the calculation data on an unsteady flow around a circular cylinder obtained using the VP2/3 and FLUENT packages and the Spalart-Allmaras and Menter turbulence models. Journal of Engineering Physics and Thermophysics, 78, pp. 1199–1213, 2005. [Crossref]
[12] Lysenko, D., Ertesvag, I. & Rian, K., Towards simulations of far-field aerodynamic sound from a circular cylinder using OpenFOAM. International Journal of Aeroacous- tics, 14(1), pp. 141–168, 2014.
[13] Crivellini, A., D’Alessandro, V. & Bassi, F., Assessment of a high-order discontinu- ous Galerkin method for incompressible three-dimensional Navier-Stokes equations: Benchmark results for the flow past a sphere up to Re=500. Computers & Fluids, 86, pp. 442–458, 2013. [Crossref]
[14] Costantinescu, G. & Squires, K., LES and DES investigations of turbulent flow over a sphere. AIAA Paper 2000-00540, AIAA, 2000.
[15] Johnson, T. & Pathel, V., Flow past a sphere up to reynolds number of 300. Journal of Fluid Mechanics, 378(1), pp. 19–70, 1999. [Crossref]
[16] Ploumhans, P., Wincklemans, G., Salmon, J., Leonard, A. & Warren, M., Vortex meth- ods for direct numerical simulation of three-dimensional bluff body flows: applications to the at Re=300,500 and 1000. Journal of Computational Physics, 178, pp. 427–463, 2002. [Crossref]
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Open Access
Research article

Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes

v. d’alessandro,
a. zoppi,
l. binci,
r. ricci
Dipartimento di Ingegneria Industriale e Scienze Matematiche Università Politecnica delle Marche Via Brecce Bianche 1, 60131 Ancona (AN), Italy
International Journal of Computational Methods and Experimental Measurements
|
Volume 4, Issue 4, 2016
|
Pages 594-603
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
View Full Article|Download PDF

Abstract:

Nowadays open-source CFD codes provide suitable environments for implementation and testing low-dissipative algorithms typically used for turbulence simulation. Moreover these codes produce a reliable tool to test high-fidelity numerics on unstructured grids, which are particularly appealing for industrial applications. Therefore in this work we have developed several solvers for incompressible Navier-Stokes equations (NSE) based on high-order explicit and implicit Runge-Kutta (RK) schemes for time-integration. Note that for NSE space discretization the numerical technology available within OpenFOAM (Open-source Field Operation And Manipulation) library was used.

Specifically in this work we have considered explicit RK projected type schemes for index 2 DAE system and L-stable Singly Diagonally Implicit Runge-Kutta (SDIRK) techniques. In the latter case an iterated PISO-like procedure based on Rhie-Chow correction was used for handling pressure-velocity coupling within each RK stage. The accuracy of the considered algorithms was evaluated studying the Taylor-Green vortex. Moreover several benchmark solutions have been computed in order to assess the reliability, the accuracy and the robustness of the presented solvers.

Keywords: Runge–Kutta schemes, Incompressible Navier–Stokes, Equations, OpenFOAM

1. Introduction

2. Numerical Approximation of Incompressible Navier–Stokes Equations

3. Result

4. Conclusions

References
[1] Vuorinen, V., Keskinen, J.P., Duwig, C. & Boersma, B., On the implementation of low-dissipative Runge-Kutta projection methods for time dependent flows using Open- FOAM. Computers & Fluids, 93, pp. 153–163, 2014. [Crossref]
[2] Shen, C., Sun, F. & Xia, X., Implementation of density-based solver for all speeds in the framework of OpenFOAM. Computer Physics Communications, 185(10), pp. 2730–2741, 2014. [Crossref]
[3] Sanderse, B. & Koren, B., Accuracy analysis of explicit Runge-Kutta methods applied to the incompressible Navier-Stokes equations. Journal of Computational Physics, 231(8), pp. 3041–3063, 2012. [Crossref]
[4] Kazemi-Kamyab, V., van Zuijlen, A. & Bijl, H., Analysis and application of high order implicit Runge-Kutta schemes to collocated finite volume discretization of the incom- pressible Navier-Stokes equations. Computers and Fluids, 109, pp. 107–115, 2015. [Crossref]
[5] Alexander, R., Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s. SIAM Jour- nal on Numerical Analysis, 14, pp. 1006–1021, 1977. [Crossref]
[6] Hairer, E. & Wanner, G., Solving Ordinary Differential Equation II, 2010.
[7] Erturk, E., Corke, T. & Gokcol, C., Numerical solutions of 2-D steady incompress- ible driven cavity flow at high reynolds numbers. International Journal for Numerical Methods in Fluids, 72, pp. 1490–1512, 2007.
[8] Botella, O. & Peyret, R., Benchmark spectral results on the lid-driven cavity flow. Com- puters & Fluids, 27(4), pp. 421–433, 1998. [Crossref]
[9] Inoue, O. & Hatakeyama, N., Sound generation by a two-dimensional circular cylinder in a uniform flow. Journal of Fluid Mechanics, 471, pp. 285–314, 2002. [Crossref]
[10] Muller, B., High order numerical simulation of aeolian tones. Computers & Fluids, 37,
pp. 450–462, 2008. [Crossref]
[11] Isaev, S.A., Baranov, P., Kudrayavtsev, N., Lysenko, D. & Usachev, A., Comparative analysis of the calculation data on an unsteady flow around a circular cylinder obtained using the VP2/3 and FLUENT packages and the Spalart-Allmaras and Menter turbulence models. Journal of Engineering Physics and Thermophysics, 78, pp. 1199–1213, 2005. [Crossref]
[12] Lysenko, D., Ertesvag, I. & Rian, K., Towards simulations of far-field aerodynamic sound from a circular cylinder using OpenFOAM. International Journal of Aeroacous- tics, 14(1), pp. 141–168, 2014.
[13] Crivellini, A., D’Alessandro, V. & Bassi, F., Assessment of a high-order discontinu- ous Galerkin method for incompressible three-dimensional Navier-Stokes equations: Benchmark results for the flow past a sphere up to Re=500. Computers & Fluids, 86, pp. 442–458, 2013. [Crossref]
[14] Costantinescu, G. & Squires, K., LES and DES investigations of turbulent flow over a sphere. AIAA Paper 2000-00540, AIAA, 2000.
[15] Johnson, T. & Pathel, V., Flow past a sphere up to reynolds number of 300. Journal of Fluid Mechanics, 378(1), pp. 19–70, 1999. [Crossref]
[16] Ploumhans, P., Wincklemans, G., Salmon, J., Leonard, A. & Warren, M., Vortex meth- ods for direct numerical simulation of three-dimensional bluff body flows: applications to the at Re=300,500 and 1000. Journal of Computational Physics, 178, pp. 427–463, 2002. [Crossref]
Cite this:
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D’Alessandro, V ., Zoppi, A., Binci, L., & Ricci, R. (2016). Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes. Int. J. Comput. Methods Exp. Meas., 4(4), 594-603. https://doi.org/10.2495/CMEM-V4-N4-594-603
V. D’Alessandro, A. Zoppi, L. Binci, and R. Ricci, "Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes," Int. J. Comput. Methods Exp. Meas., vol. 4, no. 4, pp. 594-603, 2016. https://doi.org/10.2495/CMEM-V4-N4-594-603
@research-article{D’alessandro2016DevelopmentOO,
title={Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes},
author={V. D’Alessandro and A. Zoppi and L. Binci and R. Ricci},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2016},
page={594-603},
doi={https://doi.org/10.2495/CMEM-V4-N4-594-603}
}
V. D’Alessandro, et al. "Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes." International Journal of Computational Methods and Experimental Measurements, v 4, pp 594-603. doi: https://doi.org/10.2495/CMEM-V4-N4-594-603
V. D’Alessandro, A. Zoppi, L. Binci and R. Ricci. "Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes." International Journal of Computational Methods and Experimental Measurements, 4, (2016): 594-603. doi: https://doi.org/10.2495/CMEM-V4-N4-594-603
D’ALESSANDRO V， ZOPPI A， BINCI L， et al. Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-Order Runge–kutta Schemes[J]. International Journal of Computational Methods and Experimental Measurements， 2016， 4(4)： 594-603. https://doi.org/10.2495/CMEM-V4-N4-594-603