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Projective integration for hyperbolic Shallow Water Moment Equations

Amrita Amrita and Julian Köllermeier (UGent)
(2022) AXIOMS. 11(5).
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Abstract
In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more complex PDE system. The resulting equations can become stiff depending on the friction parameters, which leads to severe time step constraints of standard numerical schemes. In this paper, we apply Projective Integration schemes to stiff Shallow Water Moment Equations to overcome the time step constraints in the stiff regime and accelerate the numerical computations while still achieving high accuracy. In different dam break and smooth wave test cases, we obtain a speedup of up to 55 with respect to standard schemes.
Keywords
shallow water equations, moment equations, stiffness, spectral gap, projective integration, SCHEMES

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Citation

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MLA
Amrita, Amrita, and Julian Köllermeier. “Projective Integration for Hyperbolic Shallow Water Moment Equations.” AXIOMS, vol. 11, no. 5, 2022, doi:10.3390/axioms11050235.
APA
Amrita, A., & Köllermeier, J. (2022). Projective integration for hyperbolic Shallow Water Moment Equations. AXIOMS, 11(5). https://doi.org/10.3390/axioms11050235
Chicago author-date
Amrita, Amrita, and Julian Köllermeier. 2022. “Projective Integration for Hyperbolic Shallow Water Moment Equations.” AXIOMS 11 (5). https://doi.org/10.3390/axioms11050235.
Chicago author-date (all authors)
Amrita, Amrita, and Julian Köllermeier. 2022. “Projective Integration for Hyperbolic Shallow Water Moment Equations.” AXIOMS 11 (5). doi:10.3390/axioms11050235.
Vancouver
1.
Amrita A, Köllermeier J. Projective integration for hyperbolic Shallow Water Moment Equations. AXIOMS. 2022;11(5).
IEEE
[1]
A. Amrita and J. Köllermeier, “Projective integration for hyperbolic Shallow Water Moment Equations,” AXIOMS, vol. 11, no. 5, 2022.
@article{01JZ0AV8BEQCYH3PSA61KJN09B,
  abstract     = {{In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more complex PDE system. The resulting equations can become stiff depending on the friction parameters, which leads to severe time step constraints of standard numerical schemes. In this paper, we apply Projective Integration schemes to stiff Shallow Water Moment Equations to overcome the time step constraints in the stiff regime and accelerate the numerical computations while still achieving high accuracy. In different dam break and smooth wave test cases, we obtain a speedup of up to 55 with respect to standard schemes.}},
  articleno    = {{235}},
  author       = {{Amrita, Amrita and Köllermeier, Julian}},
  issn         = {{2075-1680}},
  journal      = {{AXIOMS}},
  keywords     = {{shallow water equations,moment equations,stiffness,spectral gap,projective integration,SCHEMES}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{27}},
  title        = {{Projective integration for hyperbolic Shallow Water Moment Equations}},
  url          = {{http://doi.org/10.3390/axioms11050235}},
  volume       = {{11}},
  year         = {{2022}},
}
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