An adaptive local time-stepping scheme for multiresolution simulations of hyperbolic conservation laws

Kaiser, J.W.J.; Hoppe, Nils; Adami, Stefan; Adams, Nikolaus A.

doi:10.1016/j.jcpx.2019.100038

Cited by 13 publications

(9 citation statements)

References 26 publications

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“…Here, we employ an improved ALTS scheme [25], where the local timesteps are adjusted after every micro time step. This is achieved by applying the averaging and prediction operation not only to conserved quantities, but also to the divergence of the numerical flux function directly.…”

Section: Multiresolution Algorithm With Adaptive Local Time Steppingmentioning

confidence: 99%

“…, l 0 } and L, with the first holding all levels and the latter holding the active levels (which change over time). The number of RK stages s, the integration weights b i and the increments k i depend on the order of the used RK scheme [25]. The maximum time step on the finest level is limited by the global Courant-Friedrichs-Lewy (CFL) criterion…”

Section: Algorithm and Implementationmentioning

confidence: 99%

“…For higher orders, however, a third permanent buffer needs to be included. The second averaging per RK-stage and the integration in halo cells, c. f. algorithm 4, is attributed to the ALTS scheme [25].…”

Section: Algorithm and Implementationmentioning

confidence: 99%

“…Such methods were first introduced for single-stage methods [22] and then extended to explicit multi-stage Runge-Kutta (RK) schemes [23]. For the latter, also adaptive time step sizes have been introduced [24,25]. In contrast to collocation methods, the support of active scales in interpolation-based wavelet MR is local.…”

Section: Introductionmentioning

confidence: 99%

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A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows

Hoppe,

Adami,

Adams

2020

Preprint

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Numerical investigation of compressible flows faces two main challenges.In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide convective, acoustic and interfacial scale ranges. The simulation of realistic three-dimensional (3D) problems with state-of-the-art finite-volume methods (FVM) based on approximate Riemann solvers with weighted non-

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Section: Multiresolution Algorithm With Adaptive Local Time Steppingmentioning

confidence: 99%

Section: Algorithm and Implementationmentioning

confidence: 99%

Section: Algorithm and Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows

Hoppe,

Adami,

Adams

2020

Preprint

Self Cite

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“…Furthermore, symmetry is preserved by mirroring and rotating the neural network input with regard to all symmetries and subsequently averaging over the predictions. The combined model is implemented into ALPACA [11,12], a block-based multiresolution compressible two-phase solver, and validated on a rising bubble test case.…”

Section: Introductionmentioning

confidence: 99%

Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Buhendwa,

Bezgin,

Adams

2021

Preprint

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Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The latter showed improvements in terms of accuracy for coarsely resolved interfaces, however at the expense of convergence and symmetry. In this work, a combined approach is proposed, adressing the aforementioned shortcomings. We focus on interface reconstruction (IR) in the level-set method, i.e. the computation of the volume fraction and apertures. The combined model consists of a classification neural network, that chooses between the conventional (linear) IR and the neural network IR depending on the local interface resolution. The proposed approach improves accuracy for coarsely resolved interfaces and recovers the conventional IR for high resolutions, yielding first order overall convergence. Symmetry is preserved by mirroring and rotating the input level-set grid and subsequently averaging the predictions. The combined model is implemented into a CFD solver and demonstrated for two-phase flows. Furthermore, we provide details of floating point symmetric implementation and computational efficiency.

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High‐order modeling of interface interactions using level sets

et al. 2022

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Most technological advancements in medicine, process and energy engineering, life and food science, mobility and environmental engineering involve mastering fluid mechanical effects. In particular, compressible flow physics including shockwaves and phase‐interface interactions exhibit multi‐scale phenomena spanning several orders of magnitude upwards from nanometer and nanosecond time scales. Clearly, detailed analysis of such effects is impossible by means of experimental techniques. On the contrary, numerical modeling and simulations allow to capture the aforementioned mechanisms and provide non‐invasive access to any quantity of interest. Yet, the complex fluid physics require powerful computational methods utilizing recent advancements for high‐order schemes. In this work, we provide an overview on latest high‐order low‐dissipation schemes using level sets to model discontinuous phase‐interface interactions.

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An adaptive local time-stepping scheme for multiresolution simulations of hyperbolic conservation laws

Cited by 13 publications

References 26 publications

A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows

A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows

Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

High‐order modeling of interface interactions using level sets

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