scholarly journals Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system

2021 ◽  
Author(s):  
Wenbin Chen ◽  
Daozhi Han ◽  
Xiaoming Wang ◽  
Yichao Zhang
Keyword(s):  
Boussinesq System ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Unconditionally Stable

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

scholarly journals Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Leo G. Rebholz
Keyword(s):  
Finite Element ◽  
Differential Operator ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Discrete Laplacian ◽  
Navier Stokes Equations ◽  
Approximate Deconvolution ◽  
Finite Element Schemes

We present enhanced physics-based finite element schemes for two families of turbulence models, the models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007), that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.

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