A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids

Howell, B.P.; Ball, G. J.

doi:10.1006/jcph.2001.6931

Cited by 75 publications

(134 citation statements)

References 36 publications

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“…The numerical scheme uses a Voronoi mesh, where each computational cell represents a control volume bounded by cell boundaries (figure 1). To calculate the numerical fluxes across the cell boundaries and update the flow properties (density, velocities, temperature and pressure), approximate Riemann solvers (Godunov-type) are used [20,36,38]. As convective flux across the control volume boundaries (e.g.…”

Section: Numerical Schemes (A) the Free-lagrange Methodsmentioning

confidence: 99%

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

et al. 2013

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This study presents the key simulation and decision stage of a multi-disciplinary project to develop a hospital device for monitoring the effectiveness of kidney stone fragmentation by shock wave lithotripsy (SWL). The device analyses, in real time, the pressure fields detected by sensors placed on the patient's torso, fields generated by the interaction of the incident shock wave, cavitation, kidney stone and soft tissue. Earlier free-Lagrange simulations of those interactions were restricted (by limited computational resources) to computational domains within a few centimetres of the stone. Later studies estimated the far-field pressures generated when those interactions involved only single bubbles. This study extends the free-Lagrange method to quantify the bubblebubble interaction as a function of their separation. This, in turn, allowed identification of the validity of using a model of non-interacting bubbles to obtain estimations of the far-field pressures from 1000 bubbles distributed within the focus of the SWL field. Up to this point in the multi-disciplinary project, the design of the clinical device had been led by the simulations. This study records the decision point when the project's direction had to be led by far more costly clinical trials instead of the relatively inexpensive simulations.

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Section: Numerical Schemes (A) the Free-lagrange Methodsmentioning

confidence: 99%

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

et al. 2013

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“…It was initially proposed in [52] and later implemented in [1,2,53]. A Beryllium shell, of an inner radius R i = 80 · 10 −3 m and an outer radius R o = 100 · 10 −3 m, has an initial radial velocity field.…”

Section: Collapse Of a Thick-walled Cylindrical Beryllium Shellmentioning

confidence: 99%

“…In addition, the axisymmetry of the solutions is quantified as in [52]. Table 6 shows the results associated to the standard, minimum and maximum deviations of the radius for each of the layers of the mesh.…”

Section: Collapse Of a Thick-walled Cylindrical Beryllium Shellmentioning

confidence: 99%

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An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

152

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A vertex centred Jameson-Schmidt-Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 [1]) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2][3][4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 [5]). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie-Grüneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

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“…The conclusion of this analysis is that even pure-Lagrangian method are neither "pure" nor "Lagrangian". Still as demonstrated, for example in [9,65,11,66,10,110] these types of methods can be very successful for particular problems, but each problem requires some special strategy to mitigate non-Lagrangian nature of Voronoi cells.…”

Section: Introductionmentioning

confidence: 99%

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Loubère

Maire

Shashkov

et al. 2010

Journal of Computational Physics

182

130

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We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.

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A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids

Cited by 75 publications

References 36 publications

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

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