Symmetry-Preserving Discretization of Heat Transfer in a Complex Turbulent Flow

Verstappen, Roel; Velde, R.M. van der

doi:10.1007/s10665-006-9035-4

Cited by 6 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(3) (4) Thus, the equations are discretized in an unstructured grid arranged by means of the finite volume method. Furthermore, a second-order conservative scheme is used for spatial discretization [19,20]. These schemes preserve the symmetrical properties of continuous differential operators and ensure both the conservation of kinetic-energetic equilibrium and the stability of the model of mining drift [21,22].…”

Section: Mathematical and Numerical Modelmentioning

confidence: 99%

CFD study to optimize the auxiliary ventilation system in an underground mine

Costa

Bascompta

Felipe

et al. 2022

DYNA

View full text Add to dashboard Cite

Four different scenarios have been studied in an underground mine, validating the results by actual data. Finding the best ventilation conditions in terms of air velocity and heat load removal. The conditions worsen as the duct is placed further from the face. While the position of the duct regarding cross-section, lower or upper side of the drift, does not give a clear conclusion about the best option, but it depends on the variable used in the analysis, either temperature, air velocity or the specific area in the working face. The findings of this study can be used to implement the most efficient auxiliary ventilation system in the mine considering the potential main issue, whether it is the working face or the place of the equipment. Besides, future scenarios can be also analysed with the model created, providing a good tool to select the auxiliary ventilation layout in each case.

show abstract

Section: Mathematical and Numerical Modelmentioning

confidence: 99%

CFD study to optimize the auxiliary ventilation system in an underground mine

Costa

Bascompta

Felipe

et al. 2022

DYNA

View full text Add to dashboard Cite

show abstract

“…These conservation properties are held if, and only if the discrete convective operator is skew-symmetric (C (u) = −C * (u)), the negative conjugate transpose of the discrete gradient operator is exactly equal to the divergence operator (− (ΩG) * = M) and the diffusive operator D, is symmetric and positivedefinite. These properties ensure both, stability and conservation of the kinetic-energy balance even at high Reynolds numbers and with coarse grids (Verstappen and Van Der Velde [11]). …”

Section: Mathematical Formulationmentioning

confidence: 99%

Direct Numerical Simulation of the turbulent natural convection flow in an open cavity of aspect ratio 4

Segura¹,

Lehmkuhl²,

Borrell³

et al. 2012

Proceeding of THMT-12. Proceedings of the Seventh International Symposium on Turbulence, Heat and Mass Transfer Palermo, Italy,

View full text Add to dashboard Cite

-In this paper, three-dimensional turbulent natural convection heat transfer in an open cavity with an isothermal wall facing the overture has been studied. The aspect ratio chosen for the cavity has been 4 to complement the studies by Trias et al. [1,2] of closed cavities with the same aspect ratio. Direct numerical simulations (DNS) of the cavity are presented and analyzed. Rayleigh numbers up to Ra = 10 12 has been considered.

show abstract

“…Experiments show exact conservation and convergence corresponding to expected order.In [42,43], a fourth-order symmetry-preserving finite-volume method is constructed using Richardson extrapolation of a second-order symmetry-preserving method [40]. The extension to unstructured collocated meshes is presented in [32], and an application can be seen in [41]. The extension to upwind discretizations was made in [39], and a discretization for the advection operator for curvilinear collocated meshes was found in [16].…”

mentioning

confidence: 99%

Symmetry-preserving finite-difference discretizations of arbitrary order on structured curvilinear staggered grids

Hof

Vuik

2019

Journal of Computational Science

View full text Add to dashboard Cite

Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and energy are proven in the same way as for the original continuous model. This paper presents a new finite-difference symmetry-preserving space discretization. Boundary conditions and time integration are not addressed. The novelty is that it combines arbitrary order of convergence, orthogonal and non-orthogonal structured curvilinear staggered meshes, and the applicability to a wide variety of continuous operators, involving chain rules and nonlinear advection, as illustrated by the shallow-water equations. Experiments show exact conservation and convergence corresponding to expected order.In [42,43], a fourth-order symmetry-preserving finite-volume method is constructed using Richardson extrapolation of a second-order symmetry-preserving method [40]. The extension to unstructured collocated meshes is presented in [32], and an application can be seen in [41]. The extension to upwind discretizations was made in [39], and a discretization for the advection operator for curvilinear collocated meshes was found in [16]. In [17], the method is extended to non-uniform structured curvilinear collocated grids by deriving a discrete product rule. Furthermore, a symmetry-preserving method that conserves mass and energy for compressible-flow equations with a state equation is described in [35]. For rectilinear grids, this method works well, but it is challenging to let this method work for unstructured grids [35]. Finally, in [26], a symmetry-preserving discretization for curvilinear collocated and rectilinear staggered meshes is found exploiting the skew-symmetric nature of the advection operator on square-root variables.Another option to preserve symmetry is to use discrete filters to regularize the convective terms of the equation [33,19]. The combination of a symmetry-preserving discretization and regularization for compressible flows is studied in [27].Mimetic finite-difference methods also mimic the important properties of differential operators. An interesting review is given in [21], and recently, a second-order mimetic discretization of the Navier-Stokes equations conserving mass, momentum, and kinetic energy was presented in [23].Castillo et al. have provided a framework for mimetic operators in [7,8]. A second-and fourthorder mimetic approach is constructed for non-uniform rectilinear staggered meshes in [1,3,9]. In [10] their method is extended to curvilinear staggered meshes, but discrete conservation of mass, momentum and energy is not shown. A second-order mimetic finite-difference method for rectilinear staggered meshes is also constructed in [28].Other mimetic finite-difference methods use algebraic topology to design and analyze compatible discrete operators corresponding to a continuous formulation [4,18,25]. In order to construct a discrete de Rham complex, certain conditions...

show abstract

Symmetry-Preserving Discretization of Heat Transfer in a Complex Turbulent Flow

Cited by 6 publications

References 22 publications

CFD study to optimize the auxiliary ventilation system in an underground mine

CFD study to optimize the auxiliary ventilation system in an underground mine

Direct Numerical Simulation of the turbulent natural convection flow in an open cavity of aspect ratio 4

Symmetry-preserving finite-difference discretizations of arbitrary order on structured curvilinear staggered grids

Contact Info

Product

Resources

About