Computation, Volume 6, Issue 3 (September 2018) – 11 articles

The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range $44\le R{e}_D\le 993$ for the large tube and $87\le R{e}_D\le 1956$ for the small tube, considerating a contraction ratio of $\beta =1.97$ . Comparison between numerical and experimental velocity profiles has shown good agreement. Full article

Film cooling enhancement by incorporating an upstream sand-dune-shaped ramp (SDSR) to the film hole exit was numerically investigated on a flat plate under typical blowing ratios ranging from 0.5 to 1.5. Three heights of SDSRs were designed: 0.25D, 0.5D, and 0.75D. The results indicated that the upstream SDSR effectively controlled the near-wall primary flow and subsequent mutual interaction with the coolant jet, which was the main mechanism of the film cooling enhancement. First, a pair of anti-kidney vortices was formed at the trailing ridges of the SDSR, which helped suppress the kidney vortex pair due to the interaction between the coolant jet and the primary flow. Second, a weak separation and a low pressure zone were induced behind the backside of the SDSR, which caused the coolant jet to spread around the film cooling hole and improve the lateral film coverage. With respect to the baseline cylindrical film cooling holes, the effect of the upstream SDSR was distinct under different blowing ratios. Under a low blowing ratio, the upstream SDSR shortened the streetwise film layer coverage in the vicinity of the film hole centerline but increased the span-wise film layer coverage. A relatively optimal ramp height seemed to be 0.5D. Under a high blowing ratio, both the streamwise and span-wise film layer coverages improved in comparison with the baseline case. The film cooling effectiveness improved gradually with increasing ramp height. Full article

The program diagonalizes the Geometric Collective Model (Bohr Hamiltonian) with generalized Gneuss–Greiner potential with terms up to the sixth power in $\beta$ . In nuclear physics, the Bohr–Mottelson model with later extensions into the rotovibrational Collective model is an important theoretical tool with predictive power and it represents a fundamental step in the education of a nuclear physicist. Nuclear spectroscopists might find it useful for fitting experimental data, reproducing spectra, EM transitions and moments and trying theoretical predictions, while students might find it useful for learning about connections between the nuclear shape and its quantum origin. Matrix elements for the kinetic energy operator and for scalar invariants as ${\beta }^2$ and ${\beta }^{3}cos\left(3\gamma \right)$ have been calculated in a truncated five-dimensional harmonic oscillator basis with a different program, checked with three different methods and stored in a matrix library for the lowest values of angular momentum. These matrices are called by the program that uses them to write generalized Hamiltonians as linear combinations of certain simple operators. Energy levels and eigenfunctions are obtained as outputs of the diagonalization of these Hamiltonian operators. Full article

The comparison of the angular light-scattering method (ALSM) and the spectral extinction method (SEM) in solving the inverse problem of aerosol size distribution (ASD) are studied. The inverse problem is solved by a SPSO-DE hybrid algorithm, which is based on the stochastic particle swarm optimization (SPSO) algorithm and differential evolution (DE) algorithm. To improve the retrieval accuracy, the sensitivity analysis of measurement signals to characteristic parameters in ASDs is studied; and the corresponding optimal measurement angle selection region for ALSM and optimal measurement wavelength selection region for SEM are proposed, respectively. Results show that more satisfactory convergence properties can be obtained by using the SPSO-DE hybrid algorithm. Moreover, short measurement wavelengths and forward measurement angles are beneficial to obtaining more accurate results. Then, common monomodal and bimodal ASDs are estimated under different random measurement errors by using ALSM and SEM, respectively. Numerical tests show that retrieval results by using ALSM show better convergence accuracy and robustness than those by using SEM, which is attributed to the distribution of the objective function value. As a whole, considering the convergence properties and the independence on prior optical information, the ALSM combined with SPSO-DE hybrid algorithm provides a more effective and reliable technique to obtain the ASDs. Full article

Blood Pressure (BP) is one of the most important physiological indicators that provides useful information in the field of health-care monitoring. Blood pressure may be measured by both invasive and non-invasive methods. A novel algorithmic approach is presented to estimate systolic and diastolic blood pressure accurately in a way that does not require any explicit user calibration, i.e., it is non-invasive and cuff-less. The approach herein described can be applied in a medical device, as well as in commercial mobile smartphones by an ad hoc developed software based on the proposed algorithm. The authors propose a system suitable for blood pressure estimation based on the PhotoPlethysmoGraphy (PPG) physiological signal sampling time-series. Photoplethysmography is a simple optical technique that can be used to detect blood volume changes in the microvascular bed of tissue. It is non-invasive since it takes measurements at the skin surface. In this paper, the authors present an easy and smart method to measure BP through careful neural and mathematical analysis of the PPG signals. The PPG data are processed with an ad hoc bio-inspired mathematical model that estimates systolic and diastolic pressure values through an innovative analysis of the collected physiological data. We compared our results with those measured using a classical cuff-based blood pressure measuring device with encouraging results of about 97% accuracy. Full article

Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous, and varying scientific applications. One of the scientific applications that SpMV is involved in is known as Configuration Interaction (CI). CI is a linear method for solving the nonrelativistic Schrödinger equation for quantum chemical multi-electron systems, and it can deal with the ground state as well as multiple excited states. In this paper, we have developed a hybrid approach in order to deal with CI sparse matrices. The proposed model includes a newly-developed hybrid format for storing CI sparse matrices on the Graphics Processing Unit (GPU). In addition to the new developed format, the proposed model includes the SpMV kernel for multiplying the CI matrix (proposed format) by a vector using the C language and the Compute Unified Device Architecture (CUDA) platform. The proposed SpMV kernel is a vector kernel that uses the warp approach. We have gauged the newly developed model in terms of two primary factors, memory usage and performance. Our proposed kernel was compared to the cuSPARSE library and the CSR5 (Compressed Sparse Row 5) format and already outperformed both. Full article

When liquids flow through a throttling element, the velocity increases and the pressure decreases. At this point, if the pressure is below the saturated vapor pressure of this liquid, the liquid will vaporize into small bubbles, causing hydraulic cavitation. In fact, a vaporization nucleus is another crucial condition for vaporizing, and particles contained in the liquid can also work as the vaporization nuclear. As a novel heat transfer medium, nanofluids have attracted the attention of many scholars. The nanoparticles contained in the nanofluids play a significant role in the vaporization of liquids. In this paper, the effects of the nanoparticles on hydraulic cavitation are investigated. Firstly, a geometric model of a perforated plate, the throttling element in this paper, is established. Then with different nanoparticle volume fractions and diameters, the nanofluids flowing through the perforated plate are numerically simulated based on a validated numerical method. The operation conditions, such as the ratio of inlet to outlet pressures and the temperature are the considered variables. Additionally, cavitation numbers under different operating conditions are achieved to investigate the effects of nanoparticles on hydraulic cavitation. Meanwhile, the contours are extracted to research the distribution of bubbles for further investigation. This study is of interest for researchers working on hydraulic cavitation or nanofluids. Full article

A model for the simulation of wind flow in complex terrain is presented based on the Reynolds averaged Navier–Stokes (RANS) equations. For the description of turbulence, the standard k-ε, the renormalization group (RNG) k-ε, and a Reynolds stress turbulence model are applied. Additional terms are implemented in the momentum equations to describe stratification of the Earth’s atmosphere and to account for the Coriolis forces driven by the Earth’s rotation, as well as for the drag force due to forested canopy. Furthermore, turbulence production and dissipation terms are added to the turbulence equations for the two-equation, as well as for the Reynolds stress models, in order to capture different types of land use. The approaches for the turbulence models are verified by means of a homogeneous canopy test case with flat terrain and constant forest height. The validation of the models is performed by investigating the WindForS wind test site. The simulation results are compared with five-hole probe velocity measurements using multipurpose airborne sensor carrier (MASC) systems (unmanned small research aircraft)—UAV at different locations for the main wind regime. Additionally, Reynolds stresses measured with sonic anemometers at a meteorological wind mast at different heights are compared with simulation results using the Reynolds stress turbulence model. Full article

The widespread use of nanofiltration and electrodialysis membrane processes is slowed down by the difficulties in predicting the membrane performances for treating streams of variable ionic compositions. Correlations between ion hydration properties and solute transfer can help to overcome this drawback. This research aims to investigate the correlation between theoretically evaluated hydration properties of major ions in solution and experimental values of neutral organic solute fluxes. In particular, ion hydration energies, coordination and hydration number and the average ion-water distance of Na⁺, Ca²⁺, Mg²⁺, Cl⁻ and SO₄²⁻ were calculated at a high quantum mechanics level and compared with experimental sugar fluxes previously reported. The properties computed by simple and not computationally expensive models were validated with information from the literature. This work discusses the correlation between the hydration energies of ions and fluxes of three saccharides, measured through nanofiltration and ionic-exchange membranes. In nanofiltration, the sugar flux increases with the presence of ions of increasing hydration energy. Instead, inverse linear correlations were found between the hydration energy and the sugar fluxes through ion exchange membranes. Finally, an empirical model is proposed for a rough evaluation of the variation in sugar fluxes as function of hydration energy for the ion exchange membranes in diffusion experiments. Full article

We study linear-quadratic stochastic optimal control problems with bilinear state dependence where the underlying stochastic differential equation (SDE) has multiscale features. We show that, in the same way in which the underlying dynamics can be well approximated by a reduced-order dynamics in the scale separation limit (using classical homogenization results), the associated optimal expected cost converges to an effective optimal cost in the scale separation limit. This entails that we can approximate the stochastic optimal control for the whole system by a reduced-order stochastic optimal control, which is easier to compute because of the lower dimensionality of the problem. The approach uses an equivalent formulation of the Hamilton-Jacobi-Bellman (HJB) equation, in terms of forward-backward SDEs (FBSDEs). We exploit the efficient solvability of FBSDEs via a least squares Monte Carlo algorithm and show its applicability by a suitable numerical example. Full article

In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz–Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples. Full article