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N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling collisionless systems. We introduce a new…

Cosmology and Nongalactic Astrophysics · Physics 2015-11-18 Oliver Hahn , Raul E. Angulo

In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…

Numerical Analysis · Mathematics 2022-11-04 Rostislav-Paul Wilhelm , Matthias Kirchhart

The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects…

Optimization and Control · Mathematics 2024-07-11 Jan Bartsch , Patrik Knopf , Stefania Scheurer , Jörg Weber

We discuss a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis. We describe a semi-implicit time discretization that extends the range of numerical…

Plasma Physics · Physics 2013-12-19 Enrico Camporeale , Gian Luca Delzanno , Benjamin K. Bergen , J. David Moulton

The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…

Numerical Analysis · Mathematics 2025-08-08 Junming Duan , Wasilij Barsukow , Christian Klingenberg

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitrarily…

Analysis of PDEs · Mathematics 2025-02-06 Grace Mattingly , Stephen Pankavich , Jonathan Ben-Artzi

We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains. One of the novelties of the method is that the flux fraction is computed by evaluating a previously trained neural…

Numerical Analysis · Mathematics 2025-07-08 Moreno Pintore , Bruno Després

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…

Analysis of PDEs · Mathematics 2016-04-18 Robert Glassey , Stephen Pankavich , Jack Schaeffer

In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is…

Numerical Analysis · Mathematics 2018-05-29 Francis Filbet , Chang Yang

In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and their mean value in each triangular element. This type of…

Numerical Analysis · Mathematics 2024-08-28 Rémi Abgrall , Jianfang Lin , Yongle Liu

We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…

Numerical Analysis · Mathematics 2025-02-07 Yongle Liu , Wasilij Barsukow

This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field.…

Numerical Analysis · Mathematics 2010-12-13 Nicolas Crouseilles , Thomas Respaud , Eric Sonnendrücker

The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values, based on ideas from finite volumes and finite differences. This unusual mix has been shown to work well in many…

Numerical Analysis · Mathematics 2025-07-16 Wasilij Barsukow , Christian Klingenberg , Lisa Lechner , Jan Nordström , Sigrun Ortleb , Hendrik Ranocha

Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…

Fluid Dynamics · Physics 2025-10-17 Xi Deng , Bin Xie , Omar K. Matar , Pierre Boivin

The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…

Analysis of PDEs · Mathematics 2007-05-23 Hyung Ju Hwang , Alan D. Rendall , Juan J. L. Velazquez

We present an extension of the multi-moment advection scheme (Minoshima et al., 2011, J. Comput. Phys.) to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values…

Computational Physics · Physics 2015-06-04 Takashi Minoshima , Yosuke Matsumoto , Takanobu Amano

The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value…

Numerical Analysis · Mathematics 2025-03-21 Junming Duan , Wasilij Barsukow , Christian Klingenberg

We propose a spectral method for the 1D-1V Vlasov-Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling $\alpha$ and shifting $u$ of the velocity…

Numerical Analysis · Mathematics 2023-06-02 Cecilia Pagliantini , Gian Luca Delzanno , Stefano Markidis

The Vlasov-Poisson system, modeling the evolution of non-collisional plasmas in the electrostatic limit, is approx- imated by a Semi-Lagrangian technique. Spectral methods of periodic type are implemented through a collocation approach.…

Numerical Analysis · Mathematics 2019-03-27 Lorella Fatone , Daniele Funaro , Gianmarco Manzini

The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…

Cell Behavior · Quantitative Biology 2023-06-30 Sebastian Aland , Claudia Wohlgemuth