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Extreme Natural Hazards, Disaster Risks and Societal Implications
  • Extreme Natural Hazards, Disaster Risks and Societal Implications
  • Edited by Alik Ismail-Zadeh, Jaime Urrutia Fucugauchi, Andrzej Kijko, Kuniyoshi Takeuchi, Ilya Zaliapin
  • Published online: 05 May 2014
  • Print publication: 17 April 2014
  • View description
    This book presents a unique, interdisciplinary approach to disaster risk research, combining cutting-edge natural science and social science methodologies. Bringing together leading scientists, policy makers and practitioners from around the world, it presents the risks of global hazards such as volcanoes, seismic events, landslides, hurricanes, precipitation floods and space weather, and provides real-world hazard case studies from Latin America, the Caribbean, Africa, the Middle East, Asia and the Pacific region. Avoiding complex mathematics, the authors provide insight into topics such as the vulnerability of society, disaster risk reduction policy, relations between disaster policy and climate change, adaptation to hazards, and (re)insurance approaches to extreme events. This is a key resource for academic researchers and graduate students in a wide range of disciplines linked to hazard and risk studies, including geophysics, volcanology, hydrology, atmospheric science, geomorphology, oceanography and remote sensing, and for professionals and policy makers working in disaster prevention and mitigation.
  • 3 - Finite volume method
  • Alik Ismail-Zadeh, Russian Academy of Sciences, Moscow, Paul Tackley, Eidgenössische Technische Hochschule Zürich
  • Book: Computational Methods for Geodynamics
  • Published online: 05 June 2012
  • Print publication: 22 July 2010, pp 43-62
  • View extract

    Summary

    Introduction

    The finite volume (FV) method is commonly used in computational fluid dynamics and offers an intuitive and conservative way of discretising the governing equations in a manner that combines some of the advantages of finite difference and finite element methods. The general discretisation approach is to divide the domain into control volumes and integrate the equations over each control volume, with the divergence theorem used to turn some of the volume integrals into surface integrals. The resulting discretised equations equate fluxes across control volume faces (e.g. heat fluxes) to sources and sinks inside the volume (e.g. changes in temperature), and can be solved with standard direct or iterative methods (Chapter 6). The finite volume formulation is conservative because the flux flowing across a shared volume face is the same for each adjoining volume, and this is an important property in some applications. The method can be used with unstructured grids, although this chapter focuses mainly on rectangular grids, on which the discretised equations become very similar to finite difference equations. For implementation details related to using unstructured grids the reader is referred to Versteeg and Malalasekera (2007).

    Grids and control volumes: structured and unstructured grids

    Each control volume contains a node on which scalar quantities are defined. For a simple, rectangular structured grid the node is straightforwardly located in the control volume centre, as indicated by the example in Fig. 3.1.

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