ANELASTIC VERSUS FULLY COMPRESSIBLE TURBULENT RAYLEIGH–BÉNARD CONVECTION
ANELASTIC VERSUS FULLY COMPRESSIBLE TURBULENT RAYLEIGH–BÉNARD CONVECTION
复制标题
DOI：
10.1088/0004-637x/805/1/62
复制
发表时间：
2015-01
期刊：
影响因子：
--
通讯作者：
J. Verhoeven;T. Wiesehöfer;S. Stellmach
中科院分区：
文献类型：
--
作者：
J. Verhoeven;T. Wiesehöfer;S. Stellmach
数值模拟的湍流瑞利-贝纳德对流在理想气体中，使用滞弹性近似或完全可压缩方程，进行了比较。理论上，滞弹性近似在弱超绝热系统中是成立的，系统满足ψ = Δ T /Tr <$1？>，其中Δ T？>表示对流层上的超绝热温降，Tr表示底部温度。使用直接数值模拟，进行了系统的比较滞弹性和完全可压缩对流。随着超绝热性的减小，完全可压缩的结果被发现线性收敛到滞弹性的解决方案，更大的密度对比一般提高匹配。我们的结论是，在许多太阳能和行星的应用中，超绝热预计是消失的小，与滞弹性近似得到的结果实际上是更准确的比完全可压缩的计算，通常无法达到小的数值原因。另一方面，如果所研究的天体物理系统包含π O（1）？>区域，如太阳光球层，完全可压缩的模拟具有捕获全部物理的优点。有趣的是，即使在弱超绝热区域，如太阳对流区的大部分，由于效率原因而人为地使用较大的λ值所引入的误差仍然是适度的。如果定量误差的顺序为10%是可以接受的，在这样的低膨胀率区域，我们的工作表明，完全可压缩的模拟确实可以计算更有效的比他们的滞弹性同行。
Numerical simulations of turbulent Rayleigh–Bénard convection in an ideal gas, using either the anelastic approximation or the fully compressible equations, are compared. Theoretically, the anelastic approximation is expected to hold in weakly superadiabatic systems with ϵ = Δ T / T r ≪ 1 ?> , where Δ T ?> denotes the superadiabatic temperature drop over the convective layer and Tr the bottom temperature. Using direct numerical simulations, a systematic comparison of anelastic and fully compressible convection is carried out. With decreasing superadiabaticity ϵ, the fully compressible results are found to converge linearly to the anelastic solution with larger density contrasts generally improving the match. We conclude that in many solar and planetary applications, where the superadiabaticity is expected to be vanishingly small, results obtained with the anelastic approximation are in fact more accurate than fully compressible computations, which typically fail to reach small ϵ for numerical reasons. On the other hand, if the astrophysical system studied contains ϵ ∼ O ( 1 ) ?> regions, such as the solar photosphere, fully compressible simulations have the advantage of capturing the full physics. Interestingly, even in weakly superadiabatic regions, like the bulk of the solar convection zone, the errors introduced by using artificially large values for ϵ for efficiency reasons remain moderate. If quantitative errors of the order of 10% are acceptable in such low ϵ regions, our work suggests that fully compressible simulations can indeed be computationally more efficient than their anelastic counterparts.