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A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

Published online by Cambridge University Press:  03 June 2015

Armando Coco ,
Gilda Currenti ,
Ciro Del Negro  and
Giovanni Russo
Armando Coco*
Affiliation:
Dipartimento di Scienze della Terra e Geoambientali, Università di Bari Aldo Moro, Bari, Italy Bristol University, Queens Road, Bristol BS8 1RJ, United Kingdom
Gilda Currenti*
Affiliation:
Istituto Nazionale di Geofisica e Vulcanologia, Italy
Ciro Del Negro*
Affiliation:
Istituto Nazionale di Geofisica e Vulcanologia, Italy
Giovanni Russo*
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy
*
Corresponding author.Email:Armando.Coco@bristol.ac.uk
Email:gilda.currenti@ct.ingv.it
Email:ciro.delnegro@ct.ingv.it
Email:russo@dmi.unict.it
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Abstract

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains. The technique is based on a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary geometries are defined by suitable level-set functions. The equations are discretized by classical nine-point stencil on interior points, while boundary conditions and high order reconstructions are used to define the field variables at ghost-points, which are grid nodes external to the domain with a neighbor inside the domain. The linear system arising from such discretization is solved by a multigrid strategy. The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources. The method is suitable to treat problems in which the geometry of the source often changes (explore the effects of different scenarios, or solve inverse problems in which the geometry itself is part of the unknown), since it does not require complex re-meshing when the geometry is modified. Several numerical tests are successfully performed, which asses the effectiveness of the present approach.

Keywords

74B0565N0665N5574S2074G15Linear elasticityCauchy-Navier equationsground deformationunbounded domaincoordinate transformation methodCartesian gridghost pointslevel-set methodsmultigrid
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 983 - 1009
Copyright
Copyright © Global Science Press Limited 2014

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