An anisotropic, fully adaptive algorithm for the solution of convection-dominated equations with semi-Lagrangian schemes

Carpio, Jaime; Prieto, Juan Luis Ravé

doi:10.1016/j.cma.2014.01.025

Cited by 21 publications

(20 citation statements)

References 34 publications

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“…As in the steady computations, finite elements were used for the spatial discretization. The time-marching technique employed a characteristics-Galerkin method [22,25] with a fixed time step Dt. The resulting system of linearized equations was solved at each time step using FreeFem++ [22].…”

Section: Transient Computationsmentioning

confidence: 99%

“…The apparent parabolic nature of (13) and (14) suggests a marching procedure in which (12)- (14) supplemented with (20) are integrated for increasing h subject to the boundary conditions (16). The integration must be initiated at h ( 1 using the selfsimilar profiles (25). In this scheme, the value of K corresponding to a given maximum temperature / max is obtained from (20) as an eigenvalue by imposing the condition that / c !…”

Section: / 1=4mentioning

confidence: 99%

“…Eqs. (12)-(14) must be integrated for 0 < h < p together with (20) subject to the boundary conditions (16) and to the local boundary distributions (25) and (30) at h ( 1 and p À h ( 1, respectively. In the solution, the value of K corresponding to a given / max is an eigenvalue of the problem.…”

Section: =5mentioning

confidence: 99%

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Thermal explosions in spherical vessels at large Rayleigh numbers

Iglesias

Moreno-Boza

Sánchez

et al. 2017

International Journal of Heat and Mass Transfer

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This paper investigates effects of buoyancy-driven motion on the ''slowly reacting" mode of combustion, and its thermal-explosion limits, of an initially cold gaseous mixture enclosed in a spherical vessel with a constant wall temperature. As in Frank-Kamenetskii's seminal analysis, the strong temperature dependence of the effective overall reaction is modeled with a single irreversible reaction with an Arrhenius rate having a large activation energy. Besides the classical Damköhler number Da, measuring the ratio of the heat-release rate by chemical reaction evaluated at the wall temperature to the rate of heat removal by heat conduction to the wall, the solution is seen to depend on the Rayleigh number Ra, measuring the effect of buoyancy-induced motion on the heat-transport rate. For values of Da below a critical value Da c the system evolves in a slowly reacting mode where the heat losses to the wall limit the temperature increase associated with the chemical reaction, whereas for Da > Da c the initial stage of slow reaction ends abruptly at a well-defined ignition time, at which a thermal runaway occurs. Transient numerical integrations of the initial stage of slow reaction, formulated in the distinguished limit Da $ 1 and Ra $ 1 with account taken of the effects of the temporal pressure variation, are used to investigate influences of natural convection on thermal-explosion development, including changes in ignition times for Da > Da c and modified explosion curves. Our analysis reveals that Frank-Kamenetskii's criterion for the determination of critical explosion conditions, based on the investigation of existence of steady solutions, provides values of Da c ðRaÞ that are identical to those extracted from the transient computations. Specific consideration is given to the structure of the steady solution in the asymptotic limit Ra) 1 in which the flow includes a thin chemically frozen near-wall boundary layer of downward moving cold gas bounding a central inviscid region of slowly rising reacting flow driven by the boundary-layer entrainment, with the critical explosion conditions predicted to occur for Da c $ Ra 1=4. The mathematical structure of the resulting boundary-layer problem is fundamentally similar to that found in the unrelated problem of flow in curved pipes at large Dean numbers. As in that similar problem, the boundary layer exhibits a region of recirculating flow, so that the problem must be formulated as a boundary-value problem accounting for the self-similar local solutions that exist near the upper and lower stagnation points. The problem is solved with use made of an approximate integral method. The resulting asymptotic prediction for the critical Damköhler number Da c ¼ 0:655Ra 1=4 is found to be in excellent agreement with the results obtained by integration of the complete conservation equations for Ra) 1.

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Section: Transient Computationsmentioning

confidence: 99%

Section: / 1=4mentioning

confidence: 99%

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Thermal explosions in spherical vessels at large Rayleigh numbers

Iglesias

Moreno-Boza

Sánchez

et al. 2017

International Journal of Heat and Mass Transfer

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“…A space-adaptive f nite element method, used also in our previous work [22], was employed for the numerical integration. Due to the slender shape of high Reynolds number jets and the development of thin mixing layers surrounding the jet head, anisotropic mesh elements are used in the space discretization in combination with local adaptive mesh ref nement [37], with the size of the smallest elements, located at the jet mixing layer, limited to a hundredth of the orif ce semiwidth h. The use of anisotropic mesh adaptation constitutes a major improvement with respect to our earlier work [22], which reduces the number of nodes required for the simulations and signif cantly increases the efficiency of computing. Two meshes obtained in a sample case computed with anisotropic and isotropic adaptation are compared in Fig.…”

Section: The Model Problemmentioning

confidence: 99%

Critical slot size for deflagration initiation by hot products discharge into hydrogen–air atmospheres

Carpio

Iglesias

Vera

et al. 2017

International Journal of Hydrogen Energy

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“…First [30,33,49,52], an isotropic mesh is adapted frequently in order to maintain the solution within refined regions and introduce a safety area around critical regions. Another approach is to use an unsteady mesh adaptation algorithm [14,16,20,48,54] based on local or global remeshing techniques and the estimation of the error every n flow solver iterations. If the error is greater than a prescribed threshold, the mesh is re-adapted.…”

Section: Introductionmentioning

confidence: 99%

Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries

Barral

Olivier

Alauzet

2017

Journal of Computational Physics

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Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.

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An anisotropic, fully adaptive algorithm for the solution of convection-dominated equations with semi-Lagrangian schemes

Cited by 21 publications

References 34 publications

Thermal explosions in spherical vessels at large Rayleigh numbers

Thermal explosions in spherical vessels at large Rayleigh numbers

Critical slot size for deflagration initiation by hot products discharge into hydrogen–air atmospheres

Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries

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