Convection in a coupled free flow-porous media system

McCurdy，Matthew1; Moore，Nicholas2; Wang，Xiaoming3

2019

10.1137/19M1238095

SIAM JOURNAL ON APPLIED MATHEMATICS   影响因子和分区

0036-1399

1095-712X

We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous regions, respectively. Incorporating a dynamic pressure term in the Lions interface condition (which specifies the normal force balance across the fluid-medium interface) permits an energy bound on the typically uncooperative nonlinear advection term, enabling new nonlinear stability results. Within certain regimes, the nonlinear stability thresholds agree closely with the linear ones, and we quantify the differences that exist. We then compare stability thresholds produced by several common variants of the tangential interface conditions, using both numerics and asymptotics in the small Darcy number limit. Finally, we investigate the transition between full convection and fluid-dominated convection using both numerics and a heuristic theory. This heuristic theory is based on comparing the ratio of the Rayleigh number in each domain to its corresponding critical value, and it is shown to agree reasonably well with the numerics regarding how the transition depends on the depth ratio, the Darcy number, and the thermal-diffusivity ratio.

Darcy number Linear and nonlinear stability Navier-Stokes-Darcy-Boussinesq system Superposed porous-fluid convection

EI ; SCI

英语

其他

Simons Foundation Collaboration Grants for Mathematicians[524259] ; NSFC[11871159] ; Guangdong Provincial Key Laboratory for Computational Science and Material Design[2019B030301001]

Mathematics

Mathematics, Applied

WOS:000546818400006

Society for Industrial and Applied Mathematics Publications

20195207926738

Flow of fluids ; Heat convection ; Porous materials ; Stability

Fluid Flow, General:631.1 ; Heat Transfer:641.2 ; Calculus:921.2 ; Materials Science:951

MATHEMATICS

2-s2.0-85076887700

Scopus

1.Department of Mathematics,Florida State University,Tallahassee,32306,United States
2.Department of Mathematics,Geophysical Fluid Dynamics Institute,Florida State University,Tallahassee,32306,United States
3.Department of Mathematics,Southern University of Science and Technology,Shenzhen, Guangdong,518000,China

McCurdy，Matthew,Moore，Nicholas,Wang，Xiaoming. Convection in a coupled free flow-porous media system[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2019,79(6):2313-2339.

McCurdy，Matthew,Moore，Nicholas,&Wang，Xiaoming.(2019).Convection in a coupled free flow-porous media system.SIAM JOURNAL ON APPLIED MATHEMATICS,79(6),2313-2339.

McCurdy，Matthew,et al."Convection in a coupled free flow-porous media system".SIAM JOURNAL ON APPLIED MATHEMATICS 79.6(2019):2313-2339.