Elastic wave propagation in unsaturated porous media using hybrid‐Trefftz stress elements

Moldovan, Ionuţ Dragoş; Cao, Toan Duc; Freitas, J. A. Teixeira de

doi:10.1002/nme.4566

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…At this point, one has to discuss basic features of unsaturated soil models. Several authors proceed from a so-called static gas phase and argue that this is not only easier to handle compared to the fully triphasic description but also sufficiently exact, compare, for example, Callari and Abati [25] or Moldovan et al [26]. However, using the static gas-phase model means that the gas pressure p G R is always set to the atmospheric pressure.…”

Section: Triphasic Materialsmentioning

confidence: 99%

Darcy, Forchheimer, Brinkman and Richards: classical hydromechanical equations and their significance in the light of the TPM

Ehlers

2020

Arch Appl Mech

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In hydromechanical applications, Darcy, Brinkman, Forchheimer and Richards equations play a central role when porous media flow under saturated and unsaturated conditions has to be investigated. While Darcy, Brinkman, Forchheimer and Richards found their equations mainly on the basis of flow observations in field and laboratory experiments, the modern Theory of Porous Media allows for a scientific view at these equations on the basis of precise continuum mechanical and thermodynamical investigations. The present article aims at commenting the classical equations and at deriving their counterparts by the use of the thermodynamical consistent Theory of Porous Media. This procedure will prove that the classical equations are valid under certain restrictions and that extended equations exist valid for arbitrary cases in their field.

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Section: Triphasic Materialsmentioning

confidence: 99%

Darcy, Forchheimer, Brinkman and Richards: classical hydromechanical equations and their significance in the light of the TPM

Ehlers

2020

Arch Appl Mech

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“…Finally, properties (22) and (25) cancel out all domain integral terms of Equation (31). The boundary integral form of the domain statement of the hybrid-Trefftz element thus reads (21) is constructed strictly hierarchically and does not satisfy, in general, essential boundary conditions (18) and (20). Both conditions are enforced weakly, using the functions collected in basis (23) for weighting.…”

Section: Domain Statement the Navier Equation Is Enforced In The Dommentioning

confidence: 99%

“…On the internal boundary between elements i and k, the weak enforcement of the continuity condition (20) yields…”

Section: Domain Statement the Navier Equation Is Enforced In The Dommentioning

confidence: 99%

“…The electromagnetic wave equation can be obtained in practically the same way. More complex coupled problems are also reducible to the form given by Equations – through proper extensions of the aforementioned definitions (see, for instance, the coupled gas‐fluid‐porous solid formulation given in ).…”

Section: Description Of the Problemmentioning

confidence: 99%

“…It is noted that, despite the relative simplicity of the problem , the discussion presented here is quite general and its principles applicable to most boundary value problems of hyperbolic type. Indeed, it is common for hyperbolic problems defined on complex dynamic systems to be reducible to Helmholtz equations written in terms of state field potentials, typically resulting in the state field approximation itself being some linear combination of functions of type , as shown, for instance, in .…”

Section: A Case Studymentioning

confidence: 99%

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Trefftz‐based dual reciprocity method for hyperbolic boundary value problems

Moldovan

Radu

2015

Numerical Meth Engineering

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SUMMARYA new dual reciprocity-type approach to approximating the solution of non-homogeneous hyperbolic boundary value problems is presented in this paper. Typical variants of the dual reciprocity method obtain approximate particular solutions of boundary value problems in two steps. In the first step, the source function is approximated, typically using radial basis, trigonometric or polynomial functions. In the second step, the particular solution is obtained by analytically solving the non-homogeneous equation having the approximation of the source function as the non-homogeneous term. However, the particular solution trial functions obtained in this way typically have complicated expressions and, in the case of hyperbolic problems, points of singularity. Conversely, the method presented here uses the same trial functions for both source function and particular solution approximations. These functions have simple expressions and need not be singular, unless a singular particular solution is physically justified. The approximation is shown to be highly convergent and robust to mesh distortion.Any boundary method can be used to approximate the complementary solution of the boundary value problem, once its particular solution is known. The option here is to use hybrid-Trefftz finite elements for this purpose. This option secures a domain integral-free formulation and endorses the use of super-sized finite elements as the (hierarchical) Trefftz bases contain relevant physical information on the modeled problem.

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