# American Institute of Mathematical Sciences

June  2013, 6(3): 677-685. doi: 10.3934/dcdss.2013.6.677

## Simulation of lava flows with power-law rheology

 1 Istituto Nazionale di Geofisica e Vulcanologia, Sez. di Catania, Piazza Roma 2, I-95152 Catania, Italy 2 Dipartimento di Geologia e Geofisica, Università di Bari, Via Edoardo Orabona 4, I-70125 Bari, Italy 3 Dipartimento di Fisica, Università di Bologna, Viale Carlo Berti Pichat 8, I-40127 Bologna, Italy

Received  March 2010 Revised  November 2010 Published  December 2012

In this work we studied the effect of a power-law rheology on a gravity driven lava flow. Assuming a viscous fluid with constant temperature and constant density and assuming a steady flow in an inclined rectangular channel, the equation of the motion is solved by the finite volume method and a classical iterative solutor. Comparisons with observed channeled lava flows indicate that the assumption of the power-law rheology causes relevant differences in average velocity and volume flow rate with respect to the Newtonian rheology.
Citation: Marilena Filippucci, Andrea Tallarico, Michele Dragoni. Simulation of lava flows with power-law rheology. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 677-685. doi: 10.3934/dcdss.2013.6.677
##### References:

show all references

##### References:
 [1] Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036 [2] José A. Carrillo, Yanghong Huang. Explicit equilibrium solutions for the aggregation equation with power-law potentials. Kinetic & Related Models, 2017, 10 (1) : 171-192. doi: 10.3934/krm.2017007 [3] Frank Jochmann. Power-law approximation of Bean's critical-state model with displacement current. Conference Publications, 2011, 2011 (Special) : 747-753. doi: 10.3934/proc.2011.2011.747 [4] Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan, Yixin Ni. A semismooth Newton method for solving optimal power flow. Journal of Industrial & Management Optimization, 2007, 3 (3) : 553-567. doi: 10.3934/jimo.2007.3.553 [5] Zhangxin Chen. On the control volume finite element methods and their applications to multiphase flow. Networks & Heterogeneous Media, 2006, 1 (4) : 689-706. doi: 10.3934/nhm.2006.1.689 [6] T. Tachim Medjo. On the Newton method in robust control of fluid flow. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1201-1222. doi: 10.3934/dcds.2003.9.1201 [7] Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory. An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks & Heterogeneous Media, 2011, 6 (3) : 401-423. doi: 10.3934/nhm.2011.6.401 [8] Miao Yu, Haoyang Lu, Weipeng Shang. A new iterative identification method for damping control of power system in multi-interference. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020104 [9] Alberto Bressan, Graziano Guerra. Shift-differentiabilitiy of the flow generated by a conservation law. Discrete & Continuous Dynamical Systems - A, 1997, 3 (1) : 35-58. doi: 10.3934/dcds.1997.3.35 [10] Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255 [11] Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1459-1502. doi: 10.3934/dcdsb.2018159 [12] Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks & Heterogeneous Media, 2013, 8 (1) : 9-22. doi: 10.3934/nhm.2013.8.9 [13] Anibal T. Azevedo, Aurelio R. L. Oliveira, Marcos J. Rider, Secundino Soares. How to efficiently incorporate facts devices in optimal active power flow model. Journal of Industrial & Management Optimization, 2010, 6 (2) : 315-331. doi: 10.3934/jimo.2010.6.315 [14] Evgeny I. Veremey, Vladimir V. Eremeev. SISO H-Optimal synthesis with initially specified structure of control law. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 121-138. doi: 10.3934/naco.2017009 [15] Lorena Bociu, Barbara Kaltenbacher, Petronela Radu. Preface: Introduction to the Special Volume on Nonlinear PDEs and Control Theory with Applications. Evolution Equations & Control Theory, 2013, 2 (2) : i-ii. doi: 10.3934/eect.2013.2.2i [16] Jibin Li, Yan Zhou. Bifurcations and exact traveling wave solutions for the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020113 [17] Ming Chen, Chongchao Huang. A power penalty method for the general traffic assignment problem with elastic demand. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1019-1030. doi: 10.3934/jimo.2014.10.1019 [18] Liqun Qi, Zheng yan, Hongxia Yin. Semismooth reformulation and Newton's method for the security region problem of power systems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 143-153. doi: 10.3934/jimo.2008.4.143 [19] Ming Chen, Chongchao Huang. A power penalty method for a class of linearly constrained variational inequality. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1381-1396. doi: 10.3934/jimo.2018012 [20] Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019115

2018 Impact Factor: 0.545