Abstract
In this paper, we will report our recent efforts to apply a Schur complement method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver. With the interface variable introduced in Dao et al. (A Schur complement method for compressible Navier-Stokes equations. In: Proceedings of the 20th International Conference on Domain Decomposition Methods, 2011) in the context of single phase flows, we are able to simulate two-fluid models (Ndjinga et al., Nucl. Eng. Des. 238, 2008) with various schemes such as upwind, centered or Rusanov. Moreover, we introduce a scaling strategy to improve the condition number of both the interface system and the local systems. Numerical results for the isentropic two-fluid model and the compressible Navier-Stokes equations in various 2D and 3D configurations and various schemes show that our method is robust and efficient. The scaling strategy considerably reduces the number of GMRES iterations in both interface system and local system resolutions. Comparisons of performances with classical distributed computing with up to 218 processors are also reported.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Benzi, M.: Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182, 418–477 (2002)
Bergeaud, V., Fillion, P., Dérouillat, J.: Etude bibliographique sur l’inversion parallèle des matrices ovap. Tech. rep., Rapport CS/311-1/AB06A002-010/RAP/07-065 version 1.0 (2007)
Dao, T., Ndjinga, M., Magoulès, F.: Comparison of upwind and centered schemes for low Mach number flows. In: Proceedings of the International Symposium Finite Volumes for Complex Application VI. Springer Proceedings in Mathematics, vol. 4, pp. 303–311 (2011)
Dao, T., Ndjinga, M., Magoulès, F.: A Schur complement method for compressible Navier-Stokes equations. In: Proceedings of the 20th International Conference on Domain Decomposition Methods (2011)
Dolean, V., Lanteri, S.: A domain decomposition approach to finite volume solution of the Euler equations on unstructured triangular meshes. Int. J. Numer. Methods Fluids 37(6), 625–656 (2001)
Drew, D.A., Passman, S.L.: Theory of Multicomponents Fluids. Springer, New York (1999)
Fillion, P., Chanoine, A., Dellacherie, S., Kumbaro, A.: Flica-ovap: a new platform for core thermal-hydraulic studies. In: NURETH-13 (2009)
Ishii, M.: Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles, Paris (1975)
Kruis, J.: Domain Decomposition Methods for Distributed Computing. Saxe-Coburg Publications, Stirling (2006)
Maday, Y., Magoulès, F.: Absorbing interface conditions for domain decomposition methods: a general presentation. Comput. Methods Appl. Mech. Eng. 195(29–32), 3880–3900 (2006)
Magoulès, F., Roux, F.X.: Lagrangian formulation of domain decomposition methods: a unified theory. Appl. Math. Model. 30(7), 593–615 (2006)
Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, Oxford (1999)
Smith, B., Bjorstad, P., Gropp, W.: Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, Cambridge (1996)
Toselli, A., Widlund, O.B.: Domain Decomposition Methods—Algorithms and Theory. Springer, Berlin (2005)
Toumi, I., Caruge, D.: An implicit second order method for 3d two-phase flow calculations. Nucl. Sci. Eng. 130, 213–225 (1998)
Toumi, I., Kumbaro, A.: An approximate linearized Riemann solver for a two-fluid model. J. Comput. Phys. 124, 286–300 (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Dao, TH., Ndjinga, M., Magoulès, F. (2014). A Schur Complement Method for Compressible Two-Phase Flow Models. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_73
Download citation
DOI: https://doi.org/10.1007/978-3-319-05789-7_73
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05788-0
Online ISBN: 978-3-319-05789-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)