A Newton method with adaptive finite elements for solving phase-change problems with natural convection

Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Masson, Stéphane Le

doi:10.1016/j.jcp.2014.06.036

Cited by 67 publications

(58 citation statements)

References 36 publications

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“…Figure 8 shows the repartition of the streamlines of the flow in the liquid for N = 80. Furthermore, Figure 9 shows a comparison of the horizontal velocity profile u(y) at mid-domain x = 0.5 between our results and those obtained in [11]. Then, we solve the second-order discrete problem by using the Newton method, as follows 3u w 2τ , v h + (u w ∇u k−1 , v h ) + (u k−1 ∇u w , v h ) + (ν∇u w , ∇v h )…”

Section: 13supporting

confidence: 51%

“…In this section, we consider the natural convection heat transfer, where the domain is a unit two-dimensional cavity of width L and height H. The vertical walls of the cavity are isothermal, of temperatures T h (hot) and T c (cold). We refer to [11] for the details of the geometry (see Figure 7), the boundary condition and the following scaling. In this case, the viscosity is constant and doesn't depend on the heat but the data f depends of the heat as following: f 0 = 0 and…”

Section: 13mentioning

confidence: 99%

“…Figure 10. Comparison of the horizontal velocity profile u(y) at mid-domain x = 0.5 between the scheme (5.8) and [11].…”

Section: 13mentioning

confidence: 99%

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A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

Aldbaissy

Hecht

Mansour

et al. 2018

Calcolo

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Abstract. In this article, we study the time dependent Boussinesq (buoyancy) model with nonlinear viscosity depending on the temperature. We propose and analyze first and second order numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.

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Section: 13supporting

confidence: 51%

Section: 13mentioning

confidence: 99%

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A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

Aldbaissy

Hecht

Mansour

et al. 2018

Calcolo

Self Cite

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“…The first family of approaches smooths the transition between phases, allowing for the existence of a mushy region in space where both phases coexist (i.e. enthalpy method [62,25,3,24], phase field method [57,64]). The width of this region may be thought of as a trade-off between computational cost, which is lower for fatter transition zones, and modelling accuracy, whereby the"true" model corresponds to an infinitely thin transition zone.…”

Section: Introductionmentioning

confidence: 99%

CutFEM Method for Stefan--Signorini Problems with Application in Pulsed Laser Ablation

Claus¹,

Bigot²,

Kerfriden³

2018

SIAM J. Sci. Comput.

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In this article, we develop a cut finite element method for one-phase Stefan problems with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the melting/vaporisation temperature is represented by a fictitious gas phase. The moving interface between the workpiece and the fictitious gas phase may cut arbitrarily through the elements of the finite element mesh, which remains fixed throughout the simulation, thereby circumventing the need for cumbersome re-meshing operations. The primal/dual formulation of the linear one-phase Stefan problem is recast into a primal non-linear formulation using a Nitsche-type approach, which avoids the difficulty of constructing inf-sup stable primal/dual pairs. Through the careful derivation of stabilisation terms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remains stable independently of the cut location. In addition, we obtain optimal convergence with respect to space and time refinement. Several 2D and 3D examples are proposed, highlighting the robustness and flexibility of the algorithm, together with its relevance to the field of micro-manufacturing.

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“…Such systems generate acoustic disturbances and elevated energy consumption and start to be on extreme limit of their capacity. Therefore, there has been extensive research in the field of thermal management for the cooling of such telecommunication cabinets [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Liquid cooling for mobile base station

Nörtershäuser

Masson

Volkov³

et al. 2014

2014 IEEE 36th International Telecommunications Energy Conference (INTELEC)

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Thermal management of telecommunication equipments has become a major, and becomes even more critical issue as the power dissipated by the telecommunication equipments has dramatically increased. This article describes watercooling experiments made at two levels: at the cabinet level and at the rack level. Results are analyzed considering critical components temperature and energy efficiency. Water-cooling at the cabinet levelThis first study aims at evaluating a water-cooled telecommunication cabinet with two types of exchangers: cold plates on lateral sides and rear door heat exchanger.

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A Newton method with adaptive finite elements for solving phase-change problems with natural convection

Cited by 67 publications

References 36 publications

A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

CutFEM Method for Stefan--Signorini Problems with Application in Pulsed Laser Ablation

Liquid cooling for mobile base station

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