Fictitious Region Research Articles

Reduction of nonlinear embedded boundary models for problems with evolving interfaces

Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational frameworks based on such methods seems however to be challenging. Indeed, most popular model reduction techniques are projection-based, and rely on basis functions obtained from the compression of simulation snapshots. In a traditional interface-fitted computational framework, the computation of such basis functions is straightforward, primarily because the computational domain does not contain in this case a fictitious region. This is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots. The problem is exacerbated when the interface separating both regions evolves in time. This paper addresses this issue by formulating the snapshot compression problem as a weighted low-rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots. The proposed approach is application independent and therefore comprehensive. It is successfully demonstrated for the model reduction of several two-dimensional, vortex-dominated, fluid–structure interaction problems.

Modification and application of the system analysis code ATHLET to trans-critical simulations

During the loss of coolant accident (LOCA) of supercritical water cooled reactor (SCWR), the pressure in the reactor system will undergo a rapid decrease from supercritical to subcritical condition. This process is called trans-critical transients, which is of crucial importance for the LOCA analysis of SCWR. Using the current version of system code (e.g. ATHLET, REALP), calculation will be terminated due to the abrupt change of void fraction across the critical point (22.064MPa). To solve this problem, a pseudo two-phase method is proposed by introducing a fictitious region of latent heat (enthalpy of vaporization hfg∗) at pseudo-critical temperatures. A smooth transition of void fraction can be realized by using liquid-field conservation equations at temperatures lower than the pseudo-critical temperature, and vapor-field conservation equations at temperatures higher than the pseudo-critical temperature. Adopting this method, the system code ATHLET is modified to ATHLET-SC mod 2 on the basic of the previous version ATHLET-SC mod 1 modified by Shanghai Jiao Tong University. When the fictitious region of latent heat is kept as a small region, the code can achieve an acceptable accuracy. Moreover, the ATHLET-SC mod 2 code is applied to simulate the blowdown process of a simplified model. The results achieved so far indicate a good applicability of the new modified code for the trans-critical transient.

GeoScape: An Instructional Rock Garden for Inquiry-Based Cooperative Learning Exercises in Introductory Geology Courses

GeoScape is a landscape design, consisting of colored gravel, strategically placed flagstone and boulders, and two vertical features that simulates the geology of some fictitious region (a combination of geologic features in Utah, Arizona and Nevada). The design incorporates many topographic and geologic concepts that introductory geology students are expected to understand. GeoScape is an educational tool employing “hands-on”, inquiry-based, and cooperative learning techniques to help students develop problem solving and critical thinking skills by applying their geologic knowledge to a simulated field situation. Students are charged with the task of producing topographic and geologic maps and a report on the geologic evolution of the area to help solve problems in resource exploration and geologic hazards. GeoScape illustrates three-dimensional geologic structures on a smaller scale to help students visualize concepts such as bedding tilt, plunging folds, unconformities, and stratigraphic principles. GeoScape can also be used to provide at least a simulated geologic field experience to disabled students or students taking evening classes who otherwise would be unable to participate in a traditional field exercise. GeoScape is relatively easy to build and could be constructed in a variety of areas where geologic exposures are scarce or field excursion resources are limited.

Place des études économiques dans les décisions de santé animale : exemple du rapport coût/bénéfice de l'éradication de la diarrhée virale bovine en France

To help livestock production groups to rationalise health decisions, and at the request of the Association for the certification of livestock health (Association pour la certification de la santé animale en élevage: ACERSA), an economic study was conducted to assess the possible cost-effectiveness of the eradication of bovine virus diarrhoea in France. The study was performed using a fictitious average region comprising 235,000 cattle belonging to 3,300 farms, which corresponds to one-eighty-fifth of the total cattle population of France. In the first phase of the study, the cost of the disease in this region was estimated to be approximately six million French francs (US$989,937) per year. Subsequently, the cost of an eradication strategy based on the inspection of all animals when introduced into a herd, the screening of permanently-infected immunotolerant animals (IPI) and the elimination of these animals, was evaluated at nearly eleven million francs (US$1,814,884) during the first year. Theories were then formulated regarding the time required to achieve eradication (twenty years) and to reduce the epidemiological parameters (development curve of the eradication of IPI animals and of animals which had given positive results to serological tests). The reduction in the cost of the disease as a result of the eradication policy was then simulated in accordance with the evolution of the epidemiological parameters. Finally, the cost of controlling the disease, together with the residual cost of the disease, were compared with the cost of the disease without control measures. This demonstrated that such an eradication policy would, in theory, only begin to become cost-effective after approximately fifteen years. In view of the long period required to achieve cost-effectiveness, the considerable complexity of implementing an eradication programme and imponderables (particularly concerning virus spread), the recommendation of such a course of action to cattle-breeder groups is questionable. This research demonstrates that a relatively simple economic approach can serve as a useful decision-making aid.

Modeling of natural convection in an open pit

Problems of the theoretical modeling of natural and forced heat and mass transfer in open pits are addressed in many studies, most of which use approximate approaches. Only a relatively small number of studies is based on the two- and three-dimensional navier-Stokes equations [1–5]. In [1] the spatial problem of pit ventilation is formulated taking into account the interaction of the air flow with the thermally and orographically nonuniform surface and also the moisture transfer and pollution admixture diffusion. In [2] the flow fields caused by nonuniform heating of the banks of open pits were found and the interaction between the free thermal convection and wind flow was studied. The results of numerical modeling of three-dimensional flows in open pits using the fictitious region method are discussed in [3]. The most complete description of the current state of the problem is given in the monographs [4–5], where the processes of natural air convection in open pits, the reasons for their generation, and the main schemes of open pit ventilation using wind energy, thermal effects and ventilators are considered.

Fictitious region method for one class of nonlinear boundary-value problems

We consider the application of the fictitious region method to solve one class of nonlinear boundary-value problems with nonlinearity only in the boundary condition. A rate of convergence bound is obtained.

Fictitious region method for quasilinear elliptic equations of second order

Rate of convergence bounds are established for a variant of the fictitious region method for a quasilinear elliptic equation of second order with a boundary condition of the third kind.

Method of fictitious regions for one class of fourth-order quasilinear elliptical equations

We investigate the application of the fictitious region method to fourth-order quasilinear elliptical equations with Dirichlet and Neumann conditions. Convergence bounds are established for two versions of the fictitious region method.

Method of fictitious regions for second-order quasilinear elliptical equations

We consider the application of the fictitious region method to solve the first and second boundary-value problems for a second-order quasilinear elliptical equation. Rate of convergence bounds are obtained for two versions of the fictitious region method.

Numerical analysis through algorithms for solving problems of ideal hydrodynamics

Free boundaries are a characteristic feature in many problems in ideal hydrodynamics, e.g., in jet problems. The term "free boundary" refers to parts of the boundary of the flow region which are not known in advance and on which two boundary conditions are specified: kinematic and dynamic. Free-boundary problems are usually nonlinear, difficult to analyze, and so far have been little studied, with few exceptions, despite the voluminous literature on this subject. A survey of the classical results on these problems can be found, e.g., in the monographs [1-3]. In this paper, we consider two types of ideal-fluid plane flow with internal free boundaries in a channel of a complex shape. These flows are described by elliptical equations for the stream functions. We study flow in Lavrent'ev's modified scheme [4], which joins potential and turbulent flows with an unknown separation boundary. Vorticity is defined up to a constant, which is determined from the total circulation on the boundary of the turbulent region. A numerical algorithm is constructed, based on the fictitious region method. The flow of the two-layer fluid is modeled by the Laplace equation for the stream functions. The specific feature of the problem is the presence of nonhomogeneous matching conditions on the unknown boundary. The generalized formulation of the problem and the fictitious region method produce an efficient algorithm and numerical through schemes. The nonlinear problems are solved using an iterative process of successive approximations by the nonlinearity (the free boundary). 1. Joining Problem. Consider the problem of joining potential and turbulent flows with an unknown separation boundary (Lavrent'ev's scheme [4]). The flow region is D = D o O D1, with potential flow in D O and turbulent flow in D 1. The stream function ~p is such that ~(x) = 0 for x ~ S = OD o tA OD1,

New transfer-matrix theory of linear induction machines, taking into account longitudinal and transverse ferromagnetic end effects

A new 3-dimensional theory of short-primary linear induction machines is presented. The theory almost completely incorporates both longitudinal and transverse end effects, especially including ferromagnetic end effects caused by the geometry of the primary laminated iron. The theory is based on the idea of considering two different regions of the primary iron and the airspace around it as one fictitious region having an inhomogeneous permeability, with step variations only at the four iron/air boundaries if the primary iron is assumed nonconducting. The 5-layer boundary-value problem including the fictitious layer is solved neatly in a mathematical sense using the new transfer-matrix method developed here. The theory is verified from test data on the double-sided linear induction machine at General Electric Co. The theory can very accurately predict the machine behaviour, including the vertical force, at low computational cost.

Formal equivalence of direct and indirect boundary element methods

Over the last few years the great potential of boundary element methods has become more widely recognised and it is now generally accepted that, not only can they be applied to all the classical field problems such as steady state and transient potential flow 1, elastostatics 2, elastodynamics 3 and elastoplasticity 4 but that in many cases they offer the most attractive and efficient solution technique. In addition, problems with boundaries at infinity, for which the domain solutions such as finite elements or finite differences are obviously unsuitable, present no difficulties when using boundary elements. Boundary elements can be formulated using two different approaches called the direct and indirect boundary element methods. The first of these takes the form of a statement which provides values of the solution variables at any internal field point in terms of the complete set of all the boundary data, both the essential and natural. The statement can be formulated rigorously using either an approach based on Green's theorem, or as a particular case of weighted residual methods 5. The indirect method has usually been justified on a less rigorous basis. In this case the field of interest is visualized as a region, delineated within an infinite, or semi-infinite body of the material, around which fictitious singular 'sources' are distributed at an initially unknown density such that the real, specified boundary conditions are established on the boundaries of the fictitious region. This note starts from the direct boundary element method statement for the solution of potential problems and shows how this can be transformed into the equivalent indirect statement, thereby establishing the latter rigorously. Similar arguments are then applied to a more general class of differential operators.

SUR LA REPONSE TRANSITOIRE DES FORMATIONS RESISTIVES*

ABSTRACTThis paper deals with transient response of resistive formations to pulse sources. Computation of solutions of equations such as: image is linked to computation of solutions of equations such as: image It can be used in the case where several media exist, the conductivities of which are σ1 σ2.The method consists in establishing a correspondence between the case to be dealt with and a fictitious region of space with the same interfaces, in which the propagation of a disturbance obeys Equation (2).Velocities C1 C2. are related to conductivities by the condition image At the interfaces, the distribution of incident energy between transmitted and reflected energy is related to the ratio of characteristic impedances, i.e. image in the real case (ω is the angular frequency) and C1/C2 in the fictitious case.These ratios are the same because of Equation (3).Time variation g(θ) of solution of (1) in a given point is computed from time variation of solution of (2) at the same point by means of the transformation image (in which τ is the actual time and T the time unit).Equation (4) originates from a formula of symbolic calculus, that allows the Laplace transform of F(Vp) to be calculated from the known Laplace transform of F(p). This correspondence is the one that allows passage from in (1) to in (2)Equation (4) becomes considerably simpler when the response to the unit impulse consists (as happens most often) of the sum of a finite or infinite number of pulses The results is then a sum of functions such as: image Hence, this procedure appears as an extension to systems that obey Equation (1) of the image theory very often used when Equation (2) is applied.

Some Fresh Perspectivas on Galdos' Dona Perfecta

The belief held this writer that Dofia Perfecta has too long been relegated many critics to its author's lesser works-largely because of the social thesis it sometimes too obviously embodies to the detriment of characterization-was recently strengthened the reactions of some students. Their spontaneous criticism in favor of the razdn vital, among other features, of Doiia Perfecta has shown that the stale conventionality of certain Galdosian critics regarding some of Gald6s' works needs to be questioned. If with their ignorance of a good deal of the background of Dofa Perfecta students can see something more real and valid in the novel today, why not the scholars? The reader may be wondering at the choice of the Ortegan terms perspectiva and razdn vital thus far. It is to be hoped that the reasons will become more apparent, but it should not be strange that Ortega or others of the Generation of '98 are invoked in connection with one so often hailed as a precursor of theirs. For the moment, a few more of Ortega's words may be appropriate: ... sin renunciar a la primera vista de una cuesti6n, ?por qu6 no hemos de aspirar a una segunda y a una tercera vista?'' To start with, there is in Dofia Perfecta what may be likened to the first movement of a musical composition, for in his opening chapters2 Gald6s introduces most of the themes to be developed later: the poverty of this typical though deliberately fictitious region of Spain; the ironically poetic names in this land that reflect the imagination of a Don Quijote or a Santa Teresa; the encroachment on Pepe Rey's property Licurgo and colleagues; the local violence and disregard of due process of law and governmental authority; the hero worship of Caballuco, the cacique of Orbajosa; and Pepe's reactions to these, which like the reader's, are largely unfavorable. These themes are presented mainly in dialogue form, naturally, skillfully, and with no little humor (although this may not always be intentional). One is not especially aware at first reading that they are to assume any great importance in the novel. The first principal character is Pepe Rey, who puts in an immediate appearance and is rather obviously to be the hero. His identity is quickly clarified and the purpose of his visit soon becomes apparent. As Pepe strains for a glimpse of his pretty cousin, Rosario, who blushes cherry-red at his sight, one is already prepared for what might be a trite romance. An omniscient reader could made more of certain details, such as mention of the entrance to the garden having been barred and the presence of the Penitenciario. But that would be premature. One is inclined to say with Pepe, Vamos, vamos.. . (p. 20). In Chapter III the omniscient author takes over to give some necessary background on the antecedents of the story and a character sketch of Pepe. This interruption is not so gauche as some (e.g., pp. 57, 142, 195). With the narrative and bits of description there is a good deal of dialogue, and the author does not interpose too strenuously. Intentionally or not, suspense, or impatience, is built up, for the reader perhaps feels he was doing rather nicely in discovering by himself what was happening and what Pepe was like. Further enlightened Gald6s' exposition, however, he has smiled along with the author at the contrast between the idyllic life of Orbajosa (as recalled through the