Finite element analysis of a projection-based stabilization method for the Darcy–Brinkman equations in double-diffusive convection

2013 ◽  
Vol 64 ◽  
pp. 35-49 ◽  
Author(s):  
Aytekin Çıbık ◽  
Songül Kaya
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Double Diffusive Convection ◽  
Stabilization Method ◽  
Element Analysis ◽  
Brinkman Equations ◽  
Diffusive Convection ◽  
Double Diffusive

Finite Element Study of Double Diffusive Convection and Solidification Under the Combined Influence of Microgravity and Magnetic Fields

2002 ◽  
Author(s):  
K. Li ◽  
B. Q. Li ◽  
H. C. de Groh
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Fields ◽  
Space Vehicles ◽  
Element Formulation ◽  
Double Diffusive Convection ◽  
Interface Morphology ◽  
Concentration Effects ◽  
Diffusive Convection ◽  
Double Diffusive

A finite element model is presented for the g-jitter induced double diffusive convection and solidification phenomena with and without the presence of magnetic fields in a Sn-doped Bi single crystal growth system planned for space experiments in space vehicles and the International Space Station. The model is developed based on the deforming finite element formulation with the penalty formulation for pressure approximation and an isothermal front tracking algorithm is used to predict the solid-liquid interface. Extensive numerical simulations are carried out and studied parameters include the effects of solutal striation on the solidification front location and interface morphology under both steady state and g-jitter (or time varying gravity perturbations) conditions with and without the presence of a magnetic field. Both synthesized g-jitter and real g-jitter taken from space flights are used, with the former intended to provide a fundamental understanding of system performance and later to obtain quantitative information in real flight environments. Computed results show that the concentration effects on interface morphology must be considered for an accurate prediction of solidification interface morphology. Also, an applied magnetic field can be very useful means to suppress the deleterious g-jitter induced convection and solutal striation and their effects on solidification.

POD-ROM for the Darcy–Brinkman equations with double-diffusive convection

2019 ◽  
Vol 27 (3) ◽  
pp. 123-139 ◽  
Author(s):  
Fatma G. Eroglu ◽  
Songul Kaya ◽  
Leo G. Rebholz
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Stability And Convergence ◽  
Double Diffusive Convection ◽  
Reduced Order ◽  
Brinkman Equations ◽  
Numerical Tests ◽  
Diffusive Convection ◽  
Proper Orthogonal ◽  
Double Diffusive

Abstract This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced model based on proper orthogonal decomposition, present a stability and convergence analyses for it, and give results for numerical tests on a benchmark problem which show it is an effective approach to model reduction in this setting.

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