Adaptive numerical resolution of the Vlasov equation

2009 ◽  
pp. 43-58 ◽  
Author(s):  
M. Campos Pinto ◽  
M. Mehrenberger
Keyword(s):  
Vlasov Equation ◽  
Numerical Resolution

scholarly journals A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

2011 ◽  
Vol 10 (4) ◽  
pp. 1001-1026 ◽  
Author(s):  
Nicolas Crouseilles ◽  
Thomas Respaud
Keyword(s):  
Electric Field ◽  
Vlasov Equation ◽  
Lagrangian Method ◽  
Poisson's Equation ◽  
B Spline ◽  
Charge Conservation ◽  
Numerical Resolution ◽  
Field Evolution ◽  
Runge Kutta ◽  
A Charge

AbstractIn this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson’s equation, or equivalently under charge conservation, the Ampère’s one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

scholarly journals The Semi-Lagrangian Method for the Numerical Resolution of the Vlasov Equation

1999 ◽  
Vol 149 (2) ◽  
pp. 201-220 ◽  
Author(s):  
Eric Sonnendrücker ◽  
Jean Roche ◽  
Pierre Bertrand ◽  
Alain Ghizzo
Keyword(s):  
Vlasov Equation ◽  
Lagrangian Method ◽  
Numerical Resolution

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Is there enough star formation in simulated protoclusters?

2020 ◽  
Vol 501 (2) ◽  
pp. 1803-1822
Author(s):  
Seunghwan Lim ◽  
Douglas Scott ◽  
Arif Babul ◽  
David J Barnes ◽  
Scott T Kay ◽  
...  
Keyword(s):  
Star Formation ◽  
Galaxy Formation ◽  
Star Formation History ◽  
Test Case ◽  
Numerical Resolution ◽  
Formation History ◽  
Order Of Magnitude ◽  
History Of ◽  
Hydrodynamical Simulations ◽  
Formation Efficiency

ABSTRACT As progenitors of the most massive objects, protoclusters are key to tracing the evolution and star formation history of the Universe, and are responsible for ${\gtrsim }\, 20$ per cent of the cosmic star formation at $z\, {\gt }\, 2$. Using a combination of state-of-the-art hydrodynamical simulations and empirical models, we show that current galaxy formation models do not produce enough star formation in protoclusters to match observations. We find that the star formation rates (SFRs) predicted from the models are an order of magnitude lower than what is seen in observations, despite the relatively good agreement found for their mass-accretion histories, specifically that they lie on an evolutionary path to become Coma-like clusters at $z\, {\simeq }\, 0$. Using a well-studied protocluster core at $z\, {=}\, 4.3$ as a test case, we find that star formation efficiency of protocluster galaxies is higher than predicted by the models. We show that a large part of the discrepancy can be attributed to a dependence of SFR on the numerical resolution of the simulations, with a roughly factor of 3 drop in SFR when the spatial resolution decreases by a factor of 4. We also present predictions up to $z\, {\simeq }\, 7$. Compared to lower redshifts, we find that centrals (the most massive member galaxies) are more distinct from the other galaxies, while protocluster galaxies are less distinct from field galaxies. All these results suggest that, as a rare and extreme population at high z, protoclusters can help constrain galaxy formation models tuned to match the average population at $z\, {\simeq }\, 0$.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

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