Full implicit scheme

The advantage of the full implicit scheme and the direct enforcement of the continuity equation can be more clearly seen when we formulate a suitable Poisson equation for the pressure by taking the divergence of the momentum equation, Eq. (1.2) ... 

With the semi-implidt/explicit scheme, the terms in the first parentheses of the right-hand side of Eq. (1.18) are not identically zero. However, with the full implicit scheme in which the continuity equation is satisfied with machine accuracy, these terms are zero and therefore the periodic part of the pressure is more accurately evaluated. 

Equations (4.2), (4.3), and (4.4) are for the fuel channel, water rod channel, and outside core, respectively. The governing equations are discretized using the upwind difference scheme and the full implicit scheme. The boundary conditions are the feedwater flow rate, the feedwater temperature, and the mrbine inlet flow rate. The characteristic of the turbine control valve, expressed as the change of steam flow rate, is shown in Fig. 4.4 [6]. The feedwater flow rate changes with the core pressure as shown in Fig. 4.5 [6]. 

Afterwards when the sweep formulae became customary, one began to analyze in full details two-layer implicit schemes (weighted schemes) for which R = crA. These schemes obviously represent a particular case of the scheme with R = (tAq. 

For this, it seems unreasonable to employ explicit schemes with fastly varying ingredients k(u), c(u) and f(u). The power functions of temperature reflect in full measure the diiflculties involved in such a case. For any implicit scheme one possible stability condition... 

Saad, B., Saad, M. Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media. SIAM Journal of Numerical Analysis, 1-34 (2013)... 

Full-scale treatments of correlation effects, found to be necessary to repair some of the known deficiencies of the HF model wavefunction, generally are done by Configuration Interaction theory [l),(5j. With highly developed computer codes it has been found possible to include more than 10s — 10 determinants, either explicitly or implicitly in the wavefunction expansion. Unfortunately, procedures for selecting the most important terms in the Cl expansion have proved to be a source of difficulty, despite successes of Coupled Cluster methods and related schemes (6],[7]. 

Lledos and coworkers [125] investigated several hypotheses of ISM and OSM for the hydrogenation reaction of formaldehyde catalyzed by the Shvo catalyst using a simplified model [126, 127]. They selected the two most likely hypotheses and conducted full DPT studies using the real Shvo catalyst, which confirmed the evidence obtained using the model catalyst. In all of their calculations, the solvent effect has been taken into account by means of a CPCM implicit model. The two stepwise reactions for the ISM and OSM are reported in Scheme 19. 

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