Conservative integrators for vortex blob methods on the plane

Gormezano, Cem; Nave, Jean-Christophe; Wan, Andy T. S.

doi:10.1016/j.jcp.2022.111357

Journal of Computational Physics

2022

DOI: 10.1016/j.jcp.2022.111357

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Conservative integrators for vortex blob methods on the plane

Cem Gormezano

Jean-Christophe Nave²,

Andy T. S. Wan³

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2024

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“…We will be using conservative integrators based on DMM [24,22,25]. These integrators preserve artbitrary forms of conserved quantities up to machine precision and have been recently applied to many body problems [23,9] and Hamiltonian Monte Carlo [18] and geodesics in Schwarzchild geometry [21].…”

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confidence: 99%

Conservative integrators for piecewise smooth systems with transversal dynamics

Hirani,

Wan,

Wojtalewicz

2024

JCD

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We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved quantities where its trajectories cross transversally to its interface, we combine Mannshardt's transition scheme and the Discrete Multiplier Method to obtain conservative integrators capable of preserving conserved quantities up to machine precision and accuracy order. We prove that the order of accuracy of the conservative integrators is preserved after crossing the interface in the case of codimension one number of conserved quantities. Numerical examples in two and three dimensions illustrate the preservation of accuracy order across the interface for cubic and logarithmic type conserved quantities. We observed that conservative transition schemes can prevent spurious transitions from occurring, even in the case when there are fewer conserved quantities.

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mentioning

confidence: 99%

Conservative integrators for piecewise smooth systems with transversal dynamics

Hirani,

Wan,

Wojtalewicz

2024

JCD

View full text Add to dashboard Cite

show abstract

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Conservative integrators for vortex blob methods on the plane

Cited by 1 publication

References 34 publications

Conservative integrators for piecewise smooth systems with transversal dynamics

Conservative integrators for piecewise smooth systems with transversal dynamics

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