A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
Francis Filbet,Shi Jin +1 more
TLDR
A general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations, which can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved.About:
This article is published in Journal of Computational Physics.The article was published on 2010-10-01 and is currently open access. It has received 340 citations till now. The article focuses on the topics: Nonlinear system & Navier–Stokes equations.read more
Citations
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Kinetic Theory and Fluid Dynamics
TL;DR: In this article, the authors discuss the fluid-dynamic type equations derived from the Boltzmann equation as its asymptotic behavior for small mean free path and the boundary conditions that describe the behavior of the gas in the continuum limit.
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Numerical methods for kinetic equations
Giacomo Dimarco,Lorenzo Pareschi +1 more
TL;DR: This survey considers the development and mathematical analysis of numerical methods for kinetic partial differential equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods, and an overview of the current state of the art.
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A unified gas-kinetic scheme for continuum and rarefied flows IV
TL;DR: The UGKS as discussed by the authors is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path.
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Multiphysics simulations: Challenges and opportunities
David E. Keyes,Lois Curfman McInnes,Carol S. Woodward,William Gropp,Eric Myra,Michael Pernice,John B. Bell,Jed Brown,Alain Clo,Jeffrey M. Connors,Emil M. Constantinescu,Donald Estep,Katherine J. Evans,Charbel Farhat,Ammar Hakim,Glenn E. Hammond,Glen A. Hansen,Judith Hill,Tobin Isaac,Xiangmin Jiao,Kirk E. Jordan,Dinesh K. Kaushik,Efthimios Kaxiras,Alice Koniges,Kihwan Lee,P. Aaron Lott,Qiming Lu,John H. Magerlein,Reed M. Maxwell,Michael McCourt,Miriam Mehl,Roger P. Pawlowski,Amanda Randles,Daniel R. Reynolds,Béatrice Rivière,Ulrich Rüde,Timothy D. Scheibe,John N. Shadid,Brendan Sheehan,Mark S. Shephard,Andrew R. Siegel,Barry Smith,Xian-Zhu Tang,Cian R. Wilson,Barbara Wohlmuth +44 more
TL;DR: This study considers multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural’ includes both software and hardware environments.
References
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
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A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
TL;DR: In this paper, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Small amplitude processes in charged and neutral one-component systems
TL;DR: In this article, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Book
The Boltzmann equation and its applications
TL;DR: In this article, the Boltzmann Equation for rigid spheres is used to model the dynamics of a gas of rigid spheres in phase space and to solve the problem of flow and heat transfer in regions bounded by planes or cylinders.