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Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.
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An Empirical Study of Cycle Toggling Based Laplacian Solvers
We study the performance of linear solvers for graph Laplacians based on the combinatorial cycle adjustment methodology proposed by [Kelner-Orecchia-Sidford-Zhu STOC-13]. The approach finds a dual flow solution to this linear system through a sequence of flow adjustments along cycles. We study both data structure oriented and recursive methods for handling these adjustments. The primary difficulty faced by this approach, updating and querying long cycles, motivated us to study an important special case: instances where all cycles are formed by fundamental cycles on a length n path. Our methods demonstrate significant speedups over previous implementations, and are competitive with standard numerical routines.
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- Award ID(s):
- 1637564
- PAR ID:
- 10040899
- Date Published:
- Journal Name:
- Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing
- Page Range / eLocation ID:
- 33-41
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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These files contain data supporting all results reported in Lloret et al. "A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations". In Lloret et al. we found: The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectralelement-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave- induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two- layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non- linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations. Please cite as: Lloret, P., Diamessis, P., Stastna, M., & Thomsen, G. N. (2024). Data and scripts from: A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations [Data set]. Cornell University eCommons Repository. https://doi.org/10.7298/5VKW-0303more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1137/1.9781611974690.ch4
