Establishing mesh topology in multi-material cells: Enabling technology for robust and accurate multi-material simulations

Kikinzon, Evgeny; Shashkov, Mikhail; Garimella, Rao V.

doi:10.1016/j.compfluid.2018.05.026

Cited by 9 publications

(5 citation statements)

References 20 publications

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“…Future developments of this work will mainly concern the improvements of its robustness and effectiveness through mesh optimization and smoothing techniques [56,2,50,18,66] and structure preserving algorithms [41,37,12,23,22,1,33] so that future applications will effectively target in particular supersonic flows in aerodynamics [3,64] and astrophysics [30,55,52], as well as fluid-structure interaction problems [4,40,24].…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

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

Gaburro¹,

Chiocchetti²

2022

Preprint

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“…This algorithm can provide accurate results with a lower computational cost. Kikinzon et al [38] extended the moment-of-fluid method to simultaneously establish the geometry and topology. Since the modified moment-of-fluid method does not require data from its neighbors, the modified moment-of-fluid method is well suitable for massively parallel computing.…”

Section: Multi-reconstructionmentioning

confidence: 99%

Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation

Wang

Shi

2021

Mathematics

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The Poisson surface reconstruction algorithm has become a very popular tool of reconstruction from point clouds. If we reconstruct each region separately in the process of multi-reconstruction, then the reconstructed objects may overlap with each other. In order to reconstruct multicomponent surfaces without self-intersections, we propose an efficient multi-reconstruction algorithm based on a modified vector-valued Allen–Cahn equation. The proposed algorithm produces smooth surfaces and closely preserves the original data without self-intersect. Based on operator splitting techniques, the numerical scheme is divided into one linear equation and two nonlinear equations. The linear equation is discretized using an implicit method, and the resulting discrete system of equation is solved by a fast Fourier transform. The two nonlinear equations are solved analytically due to the availability of a closed-form solution. The numerical scheme has merit in that it can be straightforwardly applied to a graphics processing unit, allowing for accelerated implementation that performs much faster than central processing unit alternatives. Various experimental, numerical results demonstrate the effectiveness and robustness of the proposed method.

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“…Numerical methods for simulating compressible multiphase flows can be generally classified into two categories depending on the approach to resolve material interfaces: Diffuse interface methods (DIM) [22,64,32,21,17,16,60,58,63,59,1,44,43,15,71,72,11] and the sharp interface methods (SIM) [33,34,18,19,37,26,25,24,46,48,20]. The present work is done in the framework of the former -DIM.…”

Section: Introductionmentioning

confidence: 99%

Diffuse interface relaxation model for two-phase compressible flows with diffusion processes

Zhang,

Menshov,

Wang

et al. 2021

Preprint

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The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase Baer-Nunziato model in the limit of complete velocity relaxation and consists of the phase mass and energy balance equations, the mixture momentum equation, and a transport equation for the volume fraction. Terms describing effects of mechanical relaxation, temperature relaxation, and thermal conduction on volume fraction evolution are derived and demonstrated to be significant for heat conduction problems. The thermal conduction leads to instantaneous thermal relaxation so that the temperature equilibrium is always maintained in the interface region with meeting the entropy relations. A numerical method is developed to solve the model governing equations that ensures the pressure-velocitytemperature (PVT) equilibrium condition in its high-order extension. We solve the hyperbolic part of the governing equations with the Godunov method with the HLLC approximate Riemann solver. The non-linear parabolic part is solved with an efficient Chebyshev explicit iterative method without dealing with large sparse matrices. To verify the model and numerical methods proposed, we demonstrate numerical results of several numerical tests such as the multiphase shock tube problem, the multiphase impact problem, and the planar ablative Rayleigh-Taylor instability problem.

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Establishing mesh topology in multi-material cells: Enabling technology for robust and accurate multi-material simulations

Cited by 9 publications

References 20 publications

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

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

Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation

Diffuse interface relaxation model for two-phase compressible flows with diffusion processes

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