Abstract
The Finite Pointset Method (FPM) is a meshfree approach to numerically solve PDEs in fluid dynamics and continuum mechanics. The geometry of the domain is represented by a cloud of numerical points carrying all the necessary information and moving with the material velocity. FPM is a generalized finite difference method as the strong solution of the considered problem is determined by direct approximation of the differential operators. One of the recent applications of FPM is the simulation of triaxial tests in soil mechanics with the material law of barodesy developed by the Division of Geotechnical and Tunnel Engineering at the University of Innsbruck. In soil mechanics the development of appropriate material laws for granular media is important for the research on their mechanical behavior and the development of suitable test procedures to classify and simulate soils.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hietel, D., Junk, M., Kuhnert, J., & Tiwari, S. (2005). Meshless methods for conservation laws. In G. Warnecke (Ed.), Analysis and numerics for conservation laws (pp. 339–362). Berlin: Springer.
Kolymbas, D. (2011). Barodesy: A new hypoplastic approach. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 1220–1240.
Kolymbas, D. (2012). Barodesy: A new constitutive frame for soils. Géotechnique Letters, 2, 17–23.
Ostermann, I., Kuhnert, J., Kolymbas, D., Chen, C-H., Polymerou, I., Šmilauer, V., et al. (2013). Meshfree generalized finite difference methods in soil mechanics - Part I: Theory. Berlin: Springer. (Submitted to International Journal on Geomathematics)
Tiwari, S., Antonov, S., Hietel, D., Kuhnert, J., & Wegener, R. (2007). A meshfree method for simulations of interactions between fluids and flexible structures. In M. Griebel & M. Schweitzer (Eds.), Meshfree methods for partial differential equations III. Berlin: Springer.
Tiwari, S., & Kuhnert, J. (2005). A numerical solution scheme for solving incompressible and low mach number flows by finite pointset method. In: M. Griebel & M. Schweitzer (Eds.), Lecture notes in computational science and engineering (Vol. 43, pp. 191–206). Berlin: Springer.
Tiwari, S., & Kuhnert, J. (2007). Modeling of two-phase flows with surface tension by finite pointset method (FPM). Journal of Computational and Applied Mathematics, 203(2), 376–386.
Acknowledgments
The authors are supported by the “Deutsche Forschungsgemeinschaft (DFG)” (project number KU 1430/7-1) in the scope of the joint research project “Untersuchungen der Anwendbarkeit von netzfreien numerischen Simulationsmethoden auf Probleme der Geotechnik und Geomechanik” in cooperation with Prof. C. Vrettos, University of Kaiserslautern, and Prof. D. Kolymbas, University of Innsbruck.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kuhnert, J., Ostermann, I. (2014). The Finite Pointset Method (FPM) and an Application in Soil Mechanics. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_176
Download citation
DOI: https://doi.org/10.1007/978-3-642-32408-6_176
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32407-9
Online ISBN: 978-3-642-32408-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)