On a Class of Implicit–Explicit Runge–Kutta Schemes for Stiff Kinetic Equations Preserving the Navier–Stokes Limit
作者: Jingwei HuXiangxiong Zhang
作者单位: 1Purdue University
刊名: Journal of Scientific Computing, 2017, Vol.73 (2-3), pp.797-818
来源数据库: Springer Journal
DOI: 10.1007/s10915-017-0499-3
关键词: Boltzmann equationBGK/ES-BGK modelsIMEX Runge–Kutta schemesCompressible Euler equationsNavier–Stokes equations35Q2065L0665L0435Q3035Q31
英文摘要: Implicit–explicit (IMEX) Runge–Kutta (RK) schemes are popular high order time discretization methods for solving stiff kinetic equations. As opposed to the compressible Euler limit (leading order asymptotics of the Boltzmann equation as the Knudsen number \(\varepsilon \) goes to zero), their asymptotic behavior at the Navier–Stokes (NS) level (next order asymptotics) was rarely studied. In this paper, we analyze a class of existing IMEX RK schemes and show that, under suitable initial conditions, they can capture the NS limit without resolving the small parameter \(\varepsilon \) , i.e., \(\varepsilon =o(\Delta t)\) , \(\Delta t^m=o(\varepsilon )\) , where m is the order of the explicit RK part in the IMEX scheme. Extensive numerical tests for BGK and ES-BGK models are performed to...
原始语种摘要: Implicit–explicit (IMEX) Runge–Kutta (RK) schemes are popular high order time discretization methods for solving stiff kinetic equations. As opposed to the compressible Euler limit (leading order asymptotics of the Boltzmann equation as the Knudsen number \(\varepsilon \) goes to zero), their asymptotic behavior at the Navier–Stokes (NS) level (next order asymptotics) was rarely studied. In this paper, we analyze a class of existing IMEX RK schemes and show that, under suitable initial conditions, they can capture the NS limit without resolving the small parameter \(\varepsilon \) , i.e., \(\varepsilon =o(\Delta t)\) , \(\Delta t^m=o(\varepsilon )\) , where m is the order of the explicit RK part in the IMEX scheme. Extensive numerical tests for BGK and ES-BGK models are performed to...
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影响因子:1.71 (2012)

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关键词翻译
关键词翻译
  • B类放大器、 C类放大器 现行
  • compressible 可压缩性的
  • Euler 欧拉
  • discretization 离散化
  • explicit 明白
  • equation 方程
  • Delta 三角洲
  • popular 普及
  • existing 现行
  • Class 现行
  • limit 界限