Finite-volume scheme for anisotropic diffusion

Es, Bram van; Koren, Barry; Blank, H. J. de

doi:10.1016/j.jcp.2015.11.041

Cited by 15 publications

(14 citation statements)

References 35 publications

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“…We also show that, the parameter ε 0 can be chosen in a wide range of values preventing the so-called locking effect [4] and securing a fast convergence of the iterations as well as a good conditioning of the linear systems. The numerical method is also free from the perpendicular dynamic pollution by the parallel one, reported by other authors in very similar frameworks [12,13,20,21].…”

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confidence: 52%

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A Two Field Iterated Asymptotic-Preserving Method for Highly Anisotropic Elliptic Equations

Deluzet¹,

Narski²

2019

Multiscale Model. Simul.

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confidence: 52%

“…for n ≥ 1, A I being the iteration operator defined by Eq. (21). The eigenvalues of A I are real and non negative (see lemma 4).…”

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confidence: 97%

A Two Field Iterated Asymptotic-Preserving Method for Highly Anisotropic Elliptic Equations

Deluzet¹,

Narski²

2019

Multiscale Model. Simul.

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“…van Es et al [48] derived FVM for homogeneous anisotropic heat diffusion for both symmetric and asymmetric schemes (as illustrated in Figure 3.8). Both schemes offer the same accuracy but require different treatments of secondary cell placements and thus grid discretisation.…”

Section: Numerical Simulations Of Thermal Anisotropymentioning

confidence: 99%

“…Note that Eilmer 4 uses the symmetric scheme for isotropic solid simulations. [48] Relatively few other studies have been published on numerical simulations of thermal anisotropy using FVM or methods other than BEM and prominently none have included the added complications of CHT. The lack of anisotropic FVM simulations has been noted by Padovan in 1974 and remains true to the time of writing.…”

Section: Numerical Simulations Of Thermal Anisotropymentioning

confidence: 99%

Numerical Modelling of Anisotropic Heat Recirculation in Microcombustors

Chong¹

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The primary motivation for this study is provided by the need for numerical simulations of anisotropic walls of microcombustors which are hypothesised to have a stabilising effect on flame temperatures in microcombustion. A literature review on the topics of wall conduction effects and heat recirculation on flame stability, anisotropic thermal conduction and heat conduction numerical methods are conducted. It is concluded that a finite volume method is most suitable for the desired purpose due to existing code infrastructure in The University of Queensland's own gas dynamics solver Eilmer, for which the capability upgrade is being designed and implemented. An implicit Euler method is selected and the method outlined and implemented using Newton's method. The implementation is verified using observed order of error (OOE). Suitable values for solver tolerances are found specific to the problem tested but also considered indicative of a reasonable range for default values. Homogeneous thermal anisotropy in the form of orthotropy is verified (using OOE via method of manufactured solutions (MMS)) and validated (using an experimental case from Hornbaker [17]). A demonstration of thermal orthotropy on a simplified microcombustor is presented, confirming that significant redirection of heat can be achieved for the purposes of improving flow preheating and reducing external heat losses. Suggestions for future work are provided; in particular, highlighting the need for completion of inhomogeneous anisotropy implementation, full thermal anisotropy (as opposed to orthotropic anisotropy) and temporal lagging.

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“…( 13), the pressure gradient at the cell faces is evaluated by central differences and the face value of local material properties are determined by harmonic means (see e.g. van Es et al [14]). Viscosity varies from cell to cell based on whether cells are occupied by resin or air:…”

Section: Pressure Equation and Face Velocitiesmentioning

confidence: 99%

Simulation of liquid composite moulding using a finite volume scheme and the level-set method

Sandberg

Hattel

Spangenberg

2019

International Journal of Multiphase Flow

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In this paper, a 2D numerical framework for the simulation of flows in porous media that are characterised by a sharp transition between the saturated and unsaturated zone is presented. Using a finite volume scheme and the level-set method, the framework is derived based on a conventional, implicit solution of Darcy's law for the pressure field, while the level-set function is advected explicitly locally at the flow front. With the main application to liquid composite moulding (LCM) in mind, the numerical framework is verified against analytical solutions, experiments, and other benchmark cases for a variety of situations that occur in this composite manufacturing process. The cases include local changes in permeability related to edge-effects, merging of flow fronts, and continuous manufacturing processes. It is highlighted that the numerical framework achieves convergence with a spatial accuracy between 1 st and 2 nd -order; the level-set operations only take about 20% of the total CPU time; and the propagation of the resin front can be achieved with CFL-sized time steps without overfilling cells and without applying any artificial smoothing.

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Finite-volume scheme for anisotropic diffusion

Cited by 15 publications

References 35 publications

A Two Field Iterated Asymptotic-Preserving Method for Highly Anisotropic Elliptic Equations

A Two Field Iterated Asymptotic-Preserving Method for Highly Anisotropic Elliptic Equations

Numerical Modelling of Anisotropic Heat Recirculation in Microcombustors

Simulation of liquid composite moulding using a finite volume scheme and the level-set method

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