Seminumerical Techniques Research Articles

Parametric Evaluation of Simultaneous Effects of Damaged Zone Parameters and Rock Strength Properties on GRC

The convergence-confinement method via the ground reaction curve (GRC) is used as the common practice of tunnel design which demands accurate determination of the stress state and material strength behavior in different zones around the tunnel section. Besides, formation of the excavation/blast-induced damaged zone (EDZ/BDZ) adds more complexity to the problem due to variation of elasticity modulus of the rock mass in this zone. As a result, advanced numerical methods via finite element/difference commercial packages or user-coded, semi-numerical techniques are required to develop the GRC, which demands a high degree of proficiency and knowledge of computational plasticity and geomechanics. In this study, a new, simple, and accurate method is proposed for prediction of GRC of circular tunnels constructed in the damaged, elastoplastic rock masses obeying softening in the plastic zone. The effects of deterioration caused by the drilling/blast in the EDZ were taken into account by assuming a reduced and varying Young’s modulus using the disturbance factor, in the form of Hoek–Brown failure criterion and the Geological Strength Index (GSI). Besides, effects of intermediate principal stress and the exponential decaying dilation parameter are taken into account thanks to adoption of the unified strength criterion (USC) as the material strength criteria. To do so, genetic algorithm (GA) via the method of evolutionary polynomial regression (EPR) is used to find a relationship between a number of 19 affecting parameters on the GRC as the input, and the internal support pressure as the target of prediction. Verification analysis was performed to verify the validity of the results using field measurements data as well as other advanced numerical studies found in the literature. Lastly, variation of the support pressure with simultaneous changes in the affecting input parameters was investigated using multivariable parametric study.

An efficient pair natural orbital based configuration interaction scheme for the calculation of open-shell ionization potentials

A spin adapted configuration interaction scheme is proposed for the evaluation of ionization potentials in α high spin open shell reference functions. There are three different ways to remove an electron from such a reference, including the removal of an alpha or a beta electron from doubly occupied or an alpha electron from singly occupied molecular orbitals. Ionization operators are constructed for each of these cases, and the resulting second quantized expressions are implemented using an automated code generator environment. To achieve greater computational efficiency, the virtual space is reduced using an averaged pair natural orbital machinery developed earlier and applied with great success in the calculation of X-ray absorption spectra [D. Manganas et al., J. Chem. Phys. A 122, 1215 (2018)]. Various approximate integral evaluation schemes including the resolution of identity and seminumerical techniques are also invoked to further enhance the computational efficiency. Although the resulting method is not particularly accurate in terms of predicting absolute energy values, with a simple shift in the ionization potentials, it is still possible to use it for the qualitative characterization of the basic features of X-ray photoionization spectra. While satellite intensities cannot be computed with the current method, the inclusion of vibrational effects using a path integral technique allows for the computation of vibrational transitions corresponding to main peaks.

On the use of seminumerical simulations in predicting the 21-cm signal from the epoch of reionization

We present a detailed comparison of three different simulations of the epoch of reionization (EoR). The radiative transfer simulation (c2-ray) among them is our benchmark. Radiative transfer codes can produce realistic results, but are computationally expensive. We compare it with two seminumerical techniques: one using the same haloes as c2-ray as its sources (Sem-Num), and one using a conditional Press–Schechter scheme (CPS+GS). These are vastly more computationally efficient than c2-ray, but use more simplistic physical assumptions. We evaluate these simulations in terms of their ability to reproduce the history and morphology of reionization. We find that both Sem-Num and CPS+GS can produce an ionization history and morphology that is very close to c2-ray, with Sem-Num performing slightly better compared to CPS+GS. We also study different redshift-space observables of the 21-cm signal from EoR: the variance, power spectrum and its various angular multipole moments. We find that both seminumerical models perform reasonably well in predicting these observables at length scales relevant for present and future experiments. However, Sem-Num performs slightly better than CPS+GS in producing the reionization history, which is necessary for interpreting the future observations. The CPS+GS scheme, however, has the advantage that it is not restricted by the mass resolution of the dark matter density field.

Peristaltic propulsion of generalized Burgers’ fluids through a non-uniform porous medium: A study of chyme dynamics through the diseased intestine

A mathematical study of the peristaltic flow of complex rheological viscoelastic fluids using the generalized fractional Burgers’ model through a non-uniform channel is presented. This model is designed to study the movement of chyme and undigested chyme (biophysical waste materials) through the small intestine to the large intestine. To simulate blockages and impedance of debris generated by cell shedding, infections, adhesions on the wall and undigested material, a drag force porous media model is utilized. This effectively mimicks resistance to chyme percolation generated by solid matrix particles in the regime. The conduit geometry is mathematically simulated as a sinusoidal propagation with linear increment in shape of the bolus along the length of channel. A modified Darcy–Brinkman model is employed to simulate the generalized flows through isotropic, homogenous porous media, a simplified but physically robust approximation to actual clinical situations. To model the rheological properties of chyme, a viscoelastic Burgers’ fluid formulation is adopted. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. Numerical and approximate analytical solutions are obtained with two semi-numerical techniques, namely the homotopy perturbation method and the variational iteration method. Visualization of the results is achieved with Mathematica software. The influence of the dominant hydromechanical and geometric parameters such as fractional viscoelastic parameters, wave number, non-uniformity constant, permeability parameter, and material constants on the peristaltic flow characteristics are depicted graphically.

Semi-computational simulation of magneto-hemodynamic flow in a semi-porous channel using optimal homotopy and differential transform methods

In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field. The two-dimensional momentum conservation partial differential equations are reduced to ordinary form incorporating Lorentizian magnetohydrodynamic body force terms. These ordinary differential equations are solved by the homotopy analysis method, the differential transform method and also a numerical method (fourth-order Runge–Kutta quadrature with a shooting method), under physically realistic boundary conditions. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. The differential transform method (DTM) does not require an auxiliary parameter and is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the velocity profiles in the channel are studied in detail. Interesting fluid dynamic characteristics are revealed and addressed. The HAM and DTM solutions are shown to both correlate well with numerical quadrature solutions, testifying to the accuracy of both HAM and DTM in nonlinear magneto-hemodynamics problems. Both these semi-numerical techniques hold excellent potential in modeling nonlinear viscous flows in biological systems.

An improved spectral homotopy analysis method for MHD flow in a semi-porous channel

In this paper we report on a novel method for solving systems of highly nonlinear differential equations by blending two recent semi-numerical techniques; the spectral homotopy analysis method and the successive linearisation method. The hybrid method converges rapidly and is an enhancement of the utility of the original spectral homotopy analysis method (Motsa et al., Commun Nonlinear Sci Numer Simul 15:2293---2302, 2010; Computer & Fluids 39:1219---1225, 2010) and an improvement on other recent semi-analytical techniques. We illustrate the application of the method by solving a system of nonlinear differential equations that govern the problem of laminar viscous flow in a semi-porous channel subject to a transverse magnetic field. A comparison with the numerical solution confirms the validity and accuracy of the technique and shows that the method converges rapidly and gives very accurate results.

On New Numerical Techniques for the MHD Flow Past a Shrinking Sheet with Heat and Mass Transfer in the Presence of a Chemical Reaction

We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness (the number of iterations required to give convergent results) of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validated using a multistep, multimethod approach comprising the use of the shooting method, the Matlab bvp4c numerical routine, and with results in the literature.

Curved Bridge Decks: Analytical Strip Solution

An “exact” solution is presented for the analysis of orthotropic curved bridge decks subjected to patch, uniform, line and concentrated loads. The bridge deck is idealized as an assemblage of radially supported curved plate elements or strips. The deflection of each plate strip is expressed as a Levy type Fourier series and the loads are expressed as a corresponding series. Concentrated loads and line loads in the tangential direction are incorporated in the solution as a discontinuity in the shear force along the load line. The convergence of this procedure is achieved by increasing the number of modes rather than the number of elements. The solution has the advantage over purely numerical or seminumerical techniques, using grid analogy or finite element techniques, in that the computational difficulties do not increase as the number of terms is increased to give increased accuracy. Tabular and graphical results are presented for bridge decks subjected to various loading conditions.

Convection in a porous cavity

Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A. We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O(A6R4). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O(R30) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.