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A second order finite-difference ghost-point method for elasticity problems on unbounded domains with applications to volcanology
Language
English
Obiettivo Specifico
4V. Vulcani e ambiente
Status
Published
JCR Journal
N/A or not JCR
Peer review journal
Yes
Title of the book
Issue/vol(year)
/16 (2014)
Pages (printed)
983-1009
Issued date
2014
Keywords
Abstract
We propose a novel nite-di erence approach for the numerical solution of linear elasticity problems in
arbitrary unbounded domains. The method is an extension of a recently proposed ghost-point method
for the Poisson equation on bounded domains with arbitrary boundary conditions (Coco, Russo, JCP,
2013) to the case of the Cauchy-Navier equations on unbounded domains. The technique is based on
a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary
geometries are de ned by suitable level-set functions. The equations are discretized by classical ninepoint
stencil on interior points, while boundary conditions and high order reconstructions are used to
de ne the eld variable at ghost-point, which are grid nodes external to the domain with a neighbor
inside the domain. The approach is then adopted to solve elasticity problems applied to volcanology
for computing the displacement caused by an underground pressure source. The method is suitable
to treat problems in which the geometry of the source often changes (explore the e ects of di erent
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 modi ed. Several numerical tests are
performed, which asses the e ectiveness of the present approach.
Keywords: Linear Elasticity, Cauchy-Navier equations, ground deformation, unbounded domain,
coordinate transformation method, Cartesian grid, Ghost points, Level-set methods
arbitrary unbounded domains. The method is an extension of a recently proposed ghost-point method
for the Poisson equation on bounded domains with arbitrary boundary conditions (Coco, Russo, JCP,
2013) to the case of the Cauchy-Navier equations on unbounded domains. The technique is based on
a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary
geometries are de ned by suitable level-set functions. The equations are discretized by classical ninepoint
stencil on interior points, while boundary conditions and high order reconstructions are used to
de ne the eld variable at ghost-point, which are grid nodes external to the domain with a neighbor
inside the domain. The approach is then adopted to solve elasticity problems applied to volcanology
for computing the displacement caused by an underground pressure source. The method is suitable
to treat problems in which the geometry of the source often changes (explore the e ects of di erent
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 modi ed. Several numerical tests are
performed, which asses the e ectiveness of the present approach.
Keywords: Linear Elasticity, Cauchy-Navier equations, ground deformation, unbounded domain,
coordinate transformation method, Cartesian grid, Ghost points, Level-set methods
Type
article
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