On the configurational-force-based r-adaptive mesh refinement in isogeometric analysis

Hénap, Gábor; Szabó, Loránd

doi:10.1016/j.finel.2016.10.002

Cited by 8 publications

(2 citation statements)

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“…Mesh refinement can be grouped into three broad categories (Mitchell & McClain, 2011). (a) r‐refinement methods (Beckett et al., 2006; Hénap & Szabó, 2017; Lang et al., 2003) increase or decrease the density of the mesh by relocating the mesh vertices, (b) h‐refinement (Kardani et al., 2012; van Zwieten et al., 2017) add new points or remove existing points from the previous mesh to increase or decrease the mesh density, and (c) p‐refinement (Panourgias et al., 2014) where the element order changes (e.g.,. from linear to quadratic to cubic etc.)…”

Section: Methodsmentioning

confidence: 99%

Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

Kourakos

Harter

2021

Water Resources Research

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The density of a numerical mesh is a key component for the quality of the numerical solution. Common methods in groundwater simulations rely on meshes generated prior to simulation, which lead to unnecessary or insufficient degrees of freedom (dofs). In this study we use Adaptive Mesh Refinement (AMR) to substitute the subjective mesh generation process with a more rigorous approach where new dofs are iteratively added to the solution of an initial coarse mesh based on a solution error estimation. The simulation is solved on a succession of meshes through which the mesh density is increased in areas of steep gradients in the solution variable. Here, we apply the approach to unconfined aquifer flow which is a non‐linear problem commonly encountered in groundwater modeling. By taking advantage of the iterative nature of AMR we arrive at an efficient solver approach. We treat the position of the unconfined boundary as an additional unknown which is estimated iteratively. The first iterations are executed rapidly as the mesh is rather coarse, while the free boundary adapts to the computed water table position as close as the mesh density allows. In this study we demonstrate the viability of the proposed unconfined aquifer simulation method to a series of 2D hypothetical examples under several conditions and stresses as well as a 3D test case. In all cases the AMR was able to automatically resolve the solution in areas with steep hydraulic head gradient, using appropriately higher density to achieve high localized refinement and accuracy.

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Section: Methodsmentioning

confidence: 99%

Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

Kourakos

Harter

2021

Water Resources Research

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“…e small strain multiphasefield model accounting for configuration forces and mechanical jump conditions was constructed [41]. e theory of configuration force based on r-adaptive mesh refinement was discussed in the context of isogeometric analysis [42].…”

Section: Introductionmentioning

confidence: 99%

Application of Configuration Force to Dynamic Crack of Shale under Hydration

Fan

Zhao

et al. 2021

Mathematical Problems in Engineering

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The natural microdefects of shale and the expansion of microcracks under hydration and overlying rock loadings are important for the wellbore stability. According to the conservation of energy, the force of the microdefects and microcracks under finite deformation is studied by the method of configuration force through the migrating control volume in the spatial observer. Under the hydration stress and rock pressure, the equation of hydration stress and its work in reference configuration has been obtained, and the equations of configuration forces and configuration moment have been established as a consequence of invariance under changes. The relationship between the configuration and deformation forces is determined by the second law. The energy dissipation equation of the crack tip has been deduced, which shows that the projection of the concentrated internal configuration body force at the crack tip in the opposite direction of the crack is equal to the energy dissipation of the crack tip per unit length. The inertial and internal parts of the concentrated configuration body force at the crack tip have been derived; it is indicated that the internal configuration force plays a leading role in the irreversible fracture process. Moreover, the energy release rate of shale under hydration is proved to depend on constitutive responses and hydration stress. In the theoretical system of configuration force, the migrating control volume at the crack tip contains inclusions, microcracks, microvoids, and heterogeneity of the rock itself. We use the configuration force theory to solve the problem of rock crack propagation and rock fracture. The factors considered are more comprehensive, which can better reflect the actual situation and provide a theoretical basis for the study of wellbore stability.

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