Summary
The paper presents common developments of solution methods for conservation laws on unstructured, hybrid grids. A time-accurate dual time stepping method for low Mach number flow is presented. A parallel, linear multigrid method has been developed for applications to complex flows. Finally a new approach for generating hybrid grids, based on level set methods is described.
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References
G. Karypis et. al. Family of multilevel partitioning algorithms. Online: http://wwwusers.cs.umn.edu/ karypis/metis/ A collection of papers is available online, 1998 – 2001.
E. Turkel: Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations, JCP,vol.72, pp 277 – 298, (1987).
A. J. Chorin: A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics, Vol 2, 12–26 (1967).
M. Breuer, D. Hanel: A Dual Time-Stepping Method for 3-D, Viscous, Incompressible Vortex Flow. Computer & Fluids, vol. 22, pp. 467–484, (1993).
D. Hanel, A. Dervieux, R. Vilsmeier, O. Gloth, C. Viozat, and L. Fournier. Development of Navier-Stokes solvers on hybrid grids. Notes on Numerical Fluid Mechanics, 66:89– 111, 1998.
E. Schall, C. Viozat, B. Koobus and A. Dervieux, Computation of low Mach thermical flows with implicit upwind methods, INRIA report, (2002).
D. Hänel, A. Dervieux, O. Gloth, L. Fournier, S. Lanteri, and R. Vilsmeier. Development of Navier-Stokes solvers on hybrid grids. Notes on Numerical Fluid Mechanics, 75:49–66, 2001.
M. H. Lallemand, H. Steve, and A. Dervieux. Unstructured multigridding by volume agglomeration: current status. Computers and Fluids, 21:397–443, 1992.
D. J. Mavriplis and V. Venkatakrishnan. Agglomeration multigrid solver for two dimensional viscous flows. Int. J. of Comp. Physics, 24:553–570, 1995.
G. Carré. An implicit multigrid method by agglomeration applied to turbulent flows. Computer & Fluids, 26:299–320, 1997.
D. J. Mavriplis. Directional agglomeration multigrid techniques for high-Reynolds number viscous flows. ICASE tech. report, 98–6, 1998.
J. Francescatto and A. Dervieux. A semi-coarsening strategy for unstructured multigrid based on agglomeration. Int. J. Numer Meth. in Fluids, 26:927–957, 1998.
D. J. Mavriplis and V. Venkatalkrishnan. A 3d agglomeration multigrid solver for the Reynolds-average Navier-Stokes equations on unstructure meshes. Int. J. for Num. Meth. in Fluids, 23:527–544, 1996.
G. Carré and S. Lanteri. Parallel linear multigrid by agglomeration for the acceleration of 3-d compressible flow calculations on unstructured meshes. Numerical Algorithms, 24:309–332, 2000.
S. Osher and J.A. Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton—Jacobi formulations. J. of Comp. Physics, 79:12–49, 1988.
Mulder, Osher, and Sethian. Computing interface motion in compressible gas dynamics. J. Comp. Phys., 100:209–228, 1992.
M. Sussman, P. Smereka, and S. Osher. A level set approach for computing solutions to incompressible two-phase flow. J. Comp. Phys., 114:146–159, 1994.
J. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.
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Häne, D., Dervieux, A., Gloth, O., Fournier, L., Lanteri, S., Vilsmeier, R. (2003). Development of Navier-Stokes Solvers on Hybrid Grids. In: Hirschel, E.H. (eds) Numerical Flow Simulation III. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45693-3_3
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DOI: https://doi.org/10.1007/978-3-540-45693-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53653-3
Online ISBN: 978-3-540-45693-3
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