A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes

Kenamond, Mark A.; Kuzmin, Dmitri; Shashkov, Mikhail

doi:10.1016/j.jcp.2021.110254

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…High-order schemes that can be seen as linear in the sense of Godunov [34], may develop spurious oscillations in presence of discontinuities. In order to prevent this phenomenon, in the case of a DG discretization we adopt an a posteriori limiting procedure based on the MOOD paradigm [15,47,31]: we first apply our unlimited ALE-DG scheme everywhere, and then (a posteriori), at the end of each timestep, we check the reliability of the obtained solution in each cell against physical and numerical admissibility criteria, such as floating point exceptions, violation of positivity or violation of a relaxed discrete maximum principle (and see [35,39] for further criteria). Next, we mark as troubled those cells where the DG solution cannot be accepted.…”

Section: A Posteriori Sub-cell Fv Limitermentioning

confidence: 99%

High-order Arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes

Gaburro¹,

Chiocchetti²

2022

Preprint

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Hyperbolic partial differential equations (PDEs) cover a wide range of interesting phenomena, from human and hearth-sciences up to astrophysics: this unavoidably requires the treatment of many space and time scales in order to describe at the same time observer-size macrostructures, multi-scale turbulent features, and also zero-scale shocks. Moreover, numerical methods for solving hyperbolic PDEs must reliably handle different families of waves: smooth rarefactions, and discontinuities of shock and contact type. In order to achieve these goals, an effective approach consists in the combination of space-time-based high-order schemes, very accurate on smooth features even on coarse grids, with Lagrangian methods, which, by moving the mesh with the fluid flow, yield highly resolved and minimally dissipative results on both shocks and contacts. However, ensuring the high quality of moving meshes is a huge challenge that needs the development of innovative and unconventional techniques. The scheme proposed here falls into the family of Arbitrary-Lagrangian-Eulerian (ALE) methods, with the unique additional freedom of evolving the shape of the mesh elements through connectivity changes. We aim here at showing, by simple and very salient examples, the capabilities of high-order ALE schemes, and of our novel technique, based on the high-order space-time treatment of topology changes.

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Section: A Posteriori Sub-cell Fv Limitermentioning

confidence: 99%

High-order Arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes

Gaburro¹,

Chiocchetti²

2022

Preprint

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“…In this order value simulation, the top and front of the model are defined as free surfaces, and the remaining surfaces of the model are set as non-reflective boundary conditions to avoid stress wave reflection at the boundary (Figure 3). Choosing the ALE (Arbitrary Lagrangian Eulerian) algorithm will realize the fluid-solid coupling dynamic analysis to overcome the numerical calculation difficulties caused by the element distortion (Kenamond et al, 2021). In this number value simulation, the total initiation time of each group of calculation models is less than 120 ms.…”

Section: Numerical Simulation Processmentioning

confidence: 99%

Study on Blasting Technology for Open-Pit Layering of Complex Mine Adjacent to High and Steep Slope

Wang

et al. 2021

Front. Earth Sci.

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In China, mining blasting vibration has seriously threatened the safety and stability of high and steep rock slopes. In this paper, taking the east mining area of Jianshan Phosphorus Mine as the research background, combined with field survey, field blasting test, numerical simulation and theoretical analysis, we systematically studied the adjacent high-steep rock slope and the layered blasting technology of complex ore. Based on wide hole spacing blasting numerical simulation and field tests, the use of 8 × 4 m hole network parameters, oblique line hole-by-hole initiation method, detonator delay using 35 ms between holes, 65 ms between rows and 500 ms within the holes, the rock mass rate was reduced and the drilling workload was decreased. In addition, regression analysis was carried out on a large amount of vibration test data, and the attenuation law and propagation law of blasting vibration of adjacent high and steep slopes were predicted, which provided a reference for mine production blasting. By establishing a mathematical model of cumulative damage of rock mass blasting, it shows that the depth of impact of mining blasting on the slope of Jianshan open-pit was 0–3.6m, but the blasting did not cause overall damage to the adjacent high and steep slopes. In the future, this model can be used to predict rock damage caused by subsequent blasting.

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“…For this reason, during the last decades many different approaches that relax the constraint of exact match between fluid flow and mesh motion have been developed, while at the same time aiming to retaining the match as closely as possible. Having considered the wide class of meshless methods and SPH methods [121,168,110], which are remarkably flexible from a geometrical point of view but are generally less accurate than their mesh-based counterparts, we focus here on the so-called Arbitrary-Lagrangian-Eulerian (ALE) schemes, introduced in their indirect form in [126,125,17] and then further developed for example in [154,18,15,10,172,109,119]. These methods alternate a Lagrangian phase with a rezoning procedure (where the mesh quality is optimized) and then a remapping phase, where the numerical solution defined on the old Lagrangian mesh is transferred onto the new optimized grid.…”

Section: Introductionmentioning

confidence: 99%

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

Gaburro

Boscheri

Chiocchetti

et al. 2020

Journal of Computational Physics

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We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving Voronoi meshes that are regenerated at each time step and which explicitly allow topology changes in time. The Voronoi tessellations are obtained from a set of generator points that move with the local fluid velocity. We employ an AREPOtype approach [1], which rapidly rebuilds a new high quality mesh exploiting the previous one, but rearranging the element shapes and neighbors in order to guarantee that the mesh evolution is robust even for vortex flows and for very long computational times. The old and new Voronoi elements associated to the same generator point are connected in space-time to construct closed space-time control volumes, whose bottom and top faces may be polygons with a different number of sides. We also need to incorporate some degenerate space-time sliver elements, which are needed in order to fill the space-time holes that arise because of the topology changes in the mesh between time t n and time t n+1 . The final ALE FV-DG scheme is obtained by a novel redesign of the high order accurate fully discrete direct ALE schemes of Boscheri and Dumbser [2,3], which have been extended here to general moving Voronoi meshes and space-time sliver elements. Our new numerical scheme is based on the integration over arbitrary shaped closed spacetime control volumes combined with a fully-discrete space-time conservation formulation of the governing hyperbolic PDE system. In this way the discrete solution is conservative and satisfies the geometric conservation law (GCL) by construction. Numerical convergence studies as well as a large set of benchmark problems for hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and robustness of the proposed method. Our numerical results clearly show that the new combination of very high order schemes with regenerated meshes that allow topology changes in each time step lead to substantial improvements over the existing state of the art in direct ALE methods.Keywords: Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes, arbitrary high order in space and time, moving Voronoi tessellations with topology change, a posteriori sub-cell finite volume limiter, fully-discrete one-step ADER approach for hyperbolic PDE, compressible Euler and MHD equations directly integrated by means of a high order fully discrete one-step ADER method. To the best knowledge of the authors, this is the first time that arbitrary high order accurate direct ALE FV and DG schemes are developed with an embedded mesh generator that builds a new mesh with a different topology at each time step. State of the artLagrangian algorithms [4,5,6,7,8,9,10,11,12] are characterized by a moving computational mesh displaced with a velocity chosen as close as possible to the local fluid velocity. In the Lagrangian description of the fluid, the ...

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A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes

Cited by 6 publications

References 23 publications

High-order Arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes

High-order Arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes

Study on Blasting Technology for Open-Pit Layering of Complex Mine Adjacent to High and Steep Slope

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

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