86 research outputs found
A dynamic subgrid-scale model for LES of the G-equation
Turbulent combustion is a difficult subject as it must deal with all of the issues found in both turbulence and combustion. (We consider only premixed flames in this paper, but some of the ideas can be applied to the non-premixed case.) As in many other fields, there are two limiting cases that are easier to deal with than the general case. These are the situations in which the chemical time scale is either much shorter or much longer than the time scale associated with the turbulence. We deal with the former case. In this limit, the flame is thin compared to the turbulence length scales and can be idealized as an infinitely thin sheet. This is commonly called the flamelet regime; it has been the subject of many papers and the basis for many models (see, e.g., Linan & Williams 1993). In the flamelet model, the local flame structure is assumed to be identical to the laminar flame structure; thus the flame propagates normal to itself at the laminar flame speed, S(sub L). This allows the use of simple approximations. For example, one expects the rate of consumption of fuel to be proportional to the area of the flame surface. This idea allowed Damkohler (1940) to propose that the wrinkled flame could be replaced by a smooth one which travels at the turbulent flame speed, S(sub T), defined by S(sub T)/S(sub L) = A(sub L) /A(sub P) where A(sub L) is the total flame surface area and AP is the area projected onto the mean direction of propagation. This relation can be expected to be valid when the flame structure is modified only slightly by the turbulence. More recent approaches have attempted to relate the turbulent flame speed to turbulence intensity, u(sub '), which presumably, characterizes the wrinkling of the flame
Symmetry preserving discretization of SL(2,R) invariant equations
Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We
show that solution methods incorporating the Lie point symmetries provide
better results than standard methods.Comment: 12 pages, 3 figures, submitted to Journal of Nonlinear Mathematical
Physic
Difference schemes with point symmetries and their numerical tests
Symmetry preserving difference schemes approximating second and third order
ordinary differential equations are presented. They have the same three or
four-dimensional symmetry groups as the original differential equations. The
new difference schemes are tested as numerical methods. The obtained numerical
solutions are shown to be much more accurate than those obtained by standard
methods without an increase in cost. For an example involving a solution with a
singularity in the integration region the symmetry preserving scheme, contrary
to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure
Lie point symmetries of differential--difference equations
We present an algorithm for determining the Lie point symmetries of
differential equations on fixed non transforming lattices, i.e. equations
involving both continuous and discrete independent variables. The symmetries of
a specific integrable discretization of the Krichever-Novikov equation, the
Toda lattice and Toda field theory are presented as examples of the general
method.Comment: 17 pages, 1 figur
Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I
We propose an algorithmic procedure i) to study the ``distance'' between an
integrable PDE and any discretization of it, in the small lattice spacing
epsilon regime, and, at the same time, ii) to test the (asymptotic)
integrability properties of such discretization. This method should provide, in
particular, useful and concrete informations on how good is any numerical
scheme used to integrate a given integrable PDE. The procedure, illustrated on
a fairly general 10-parameter family of discretizations of the nonlinear
Schroedinger equation, consists of the following three steps: i) the
construction of the continuous multiscale expansion of a generic solution of
the discrete system at all orders in epsilon, following the Degasperis -
Manakov - Santini procedure; ii) the application, to such expansion, of the
Degasperis - Procesi (DP) integrability test, to test the asymptotic
integrability properties of the discrete system and its ``distance'' from its
continuous limit; iii) the use of the main output of the DP test to construct
infinitely many approximate symmetries and constants of motion of the discrete
system, through novel and simple formulas.Comment: 34 pages, no figur
A multi-level spectral deferred correction method
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser levels are examined: reducing the degrees of freedom, reducing the order of the spatial discretization, and reducing the accuracy when solving linear systems arising in implicit temporal integration. Several numerical examples demonstrate the effect of multi-level coarsening on the convergence and cost of SDC integration. In particular, MLSDC can provide significant savings in compute time compared to SDC for a three-dimensional problem
Lysozyme transgenic goats’ milk positively impacts intestinal cytokine expression and morphology
In addition to its well-recognized antimicrobial properties, lysozyme can also modulate the inflammatory response. This ability may be particularly important in the gastrointestinal tract where inappropriate inflammatory reactions can damage the intestinal epithelium, leading to significant health problems. The consumption of milk from transgenic goats producing human lysozyme (hLZ) in their milk therefore has the potential to positively impact intestinal health. In order to investigate the effect of hLZ-containing milk on the inflammatory response, young pigs were fed pasteurized milk from hLZ or non-transgenic control goats and quantitative real-time PCR was performed to assess local expression of TNF-α, IL-8, and TGF-β1 in the small intestine. Histological changes were also investigated, specifically looking at villi width, length, crypt depth, and lamina propria thickness along with cell counts for intraepithelial lymphocytes and goblet cells. Significantly higher expression of anti-inflammatory cytokine TGF-β1 was seen in the ileum of pigs fed pasteurized milk containing hLZ (P = 0.0478), along with an increase in intraepithelial lymphocytes (P = 0.0255), and decrease in lamina propria thickness in the duodenum (P = 0.0001). Based on these results we conclude that consuming pasteurized milk containing hLZ does not induce an inflammatory response and improves the health of the small intestine in pigs
Effect of Initial Disturbance on The Detonation Front Structure of a Narrow Duct
The effect of an initial disturbance on the detonation front structure in a
narrow duct is studied by three-dimensional numerical simulation. The numerical
method used includes a high resolution fifth-order weighted essentially
non-oscillatory scheme for spatial discretization, coupled with a third order
total variation diminishing Runge-Kutta time stepping method. Two types of
disturbances are used for the initial perturbation. One is a random disturbance
which is imposed on the whole area of the detonation front, and the other is a
symmetrical disturbance imposed within a band along the diagonal direction on
the front. The results show that the two types of disturbances lead to
different processes. For the random disturbance, the detonation front evolves
into a stable spinning detonation. For the symmetrical diagonal disturbance,
the detonation front displays a diagonal pattern at an early stage, but this
pattern is unstable. It breaks down after a short while and it finally evolves
into a spinning detonation. The spinning detonation structure ultimately formed
due to the two types of disturbances is the same. This means that spinning
detonation is the most stable mode for the simulated narrow duct. Therefore, in
a narrow duct, triggering a spinning detonation can be an effective way to
produce a stable detonation as well as to speed up the deflagration to
detonation transition process.Comment: 30 pages and 11 figure
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