A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method

By K. Xu. 2001

744 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/6dff67ab4c0bff461e19494b4f044df9a21ebf1e

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Microchannel flow in the slip regime: gas-kinetic BGK–Burnett solutions (2004, methodology): “As the Knudsen number increases, such as in the regime 0.1 Kn 1.0, the difference between the BGK–Burnett and BGK–NS solutions in the mass flow rate can be clearly seen in figure 8.”
A unified gas-kinetic scheme for continuum and rarefied flows (2011, methodology): “(8) by a distribution functionf0 of the Chapman-Enskog NStype with a continuous particle velocity space [10].”
A high-order moment approach for capturing non-equilibrium phenomena in the transition regime (2009, methodology): “For many years, alternative macroscopic modelling and simulation strategies have been developed (Chapman & Cowling 1970; Muller & Ruggeri 1993; Levermore 1996; Xu 2001; Shen, Fan & Xie 2003; Sun & Boyd 2004; Baker & Hadjiconstantinou 2005; Struchtrup 2005).”
Numerical methods for kinetic equations* (2014, methodology): “This idea is at the basis of the kinetic schemes for the compressible Euler (Deshpande 1986, Perthame 1990) and Navier–Stokes equations (Xu 2001), the relaxation schemes for conservation laws (Jin and Xin 1995), and the lattice Boltzmann schemes for the incompressible Navier–Stokes equations (Succi…”
A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases (2012, methodology): “In the continuum limit, the corresponding scheme will become the gas-kinetic BGK-NS method [27].”
A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow (2005, methodology): “In terms of the flux evaluation, the current multidimensional BGK solver takes 30% more computational time than the directional splitting BGK-NS method [25].”