Segregated Runge–Kutta methods for the incompressible Navier–Stokes equations
Segregated Runge–Kutta methods for the incompressible Navier–Stokes equations
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不可压缩纳维-斯托克斯方程的分离龙格-库塔方法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Badia
中科院分区：
文献类型：
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作者：
O. Colomés;S. Badia
在这项工作中，我们提出的Runge-Kutta时间积分格式的不可压缩Navier-Stokes方程的两个显着的性质。首先，速度和压力计算在时间积分级分离，而不需要执行额外的分数阶技术，破坏高精度。其次，所提出的方法保持相同的顺序的速度和压力的精度。分离的龙格-库塔方法的动机是将投影的Navier-Stokes系统隐式-显式龙格-库塔时间积分到离散的无发散空间，并使用离散的压力泊松方程在速度-压力设置中重新陈述。我们已经分析了分离的龙格-库塔方法的离散发散约束的保持以及它们与现有半显式方法的关系（在它们的全显式版本中）。我们已经进行了详细的数值实验的一系列广泛的计划（从一阶到三阶），包括隐式和IMEX积分的粘性和对流项，不可压缩层流和湍流。在此基础上，提出了带自适应时间步长的分离型Runge-Kutta格式。版权所有© 2015约翰威利父子有限公司.
In this work, we propose Runge–Kutta time integration schemes for the incompressible Navier–Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both velocities and pressures. The segregated Runge–Kutta methods are motivated as an implicit–explicit Runge–Kutta time integration of the projected Navier–Stokes system onto the discrete divergence‐free space, and its re‐statement in a velocity–pressure setting using a discrete pressure Poisson equation. We have analysed the preservation of the discrete divergence constraint for segregated Runge–Kutta methods and their relation (in their fully explicit version) with existing half‐explicit methods. We have performed a detailed numerical experimentation for a wide set of schemes (from first to third order), including implicit and IMEX integration of viscous and convective terms, for incompressible laminar and turbulent flows. Further, segregated Runge–Kutta schemes with adaptive time stepping are proposed. Copyright © 2015 John Wiley & Sons, Ltd.
影响因子：
3.4
作者：
Gassner, Gregor J.;Beck, Andrea D.
通讯作者：
Beck, Andrea D.