On a Class of Implicit–Explicit Runge–Kutta Schemes for Stiff Kinetic Equations Preserving the Navier–Stokes Limit
 作者： Jingwei Hu,  Xiangxiong 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 equation;  BGK/ES-BGK models;  IMEX Runge–Kutta schemes;  Compressible Euler equations;  Navier–Stokes equations;  35Q20;  65L06;  65L04;  35Q30;  35Q31; 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... verify our theoretical results. 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... verify our theoretical results.

• 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