Regions Of Discontinuity Research Articles

Evaluation of a high-order central-difference solver for highly compressible flows out of thermochemical equilibrium

A high-order shock-capturing central finite-difference scheme is evaluated for numerical simulations of hypersonic high-enthalpy flows out of thermochemical equilibrium. The scheme is an extension to thermochemical out-of-equilibrium flows of the technique presented in Sciacovelli et al. (2021) for high-speed flows in chemical nonequilibrium. It relies on a standard tenth-order accurate central-difference approximation of the inviscid fluxes, supplemented with a high-order accurate nonlinear artificial dissipation term of ninth-order accuracy in smooth flow regions. Close to flow discontinuities, a shock-capturing low-order term is activated based on a highly selective shock sensor. To enable robust and non oscillatory solutions in regions of strong discontinuities of the thermodynamic variables, including the vibrational temperature, a shock detector consisting of a combination of a pressure-based term and Ducros’ vorticity/dilatation sensor is applied to all conservation equations except that of vibrational energy. For the latter, a shock sensor based on the vibrational temperature itself is adopted instead, to account for the loose coupling between vibrational energy and pressure. The accuracy and robustness of the proposed approach is demonstrated for a variety of thermochemical non-equilibrium configurations, ranging from one-dimensional benchmarks to three-dimensional turbulent flows, for which the ILES capabilities of the selective high-order numerical dissipation are also showcased.

Efficient high-order gradient-based reconstruction for compressible flows

This paper extends the gradient-based reconstruction approach of Chamarthi [1] to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same stencil as of the explicit fourth-order scheme proposed in Ref. [1], which also has low dissipation properties. The proposed method is seventh-order accurate under the assumption that the variables at the cell centres are point values. A problem-independent discontinuity detector is used to obtain high-order accuracy. Accordingly, primitive or conservative variable reconstruction is performed around regions of discontinuities, whereas smooth solution regions apply flux reconstruction. The proposed approach can still share the derivatives between the inviscid and viscous fluxes, which is the main idea behind the gradient-based reconstruction. Several standard benchmark test cases are presented. The proposed method is more efficient than the seventh-order weighted compact nonlinear scheme (WCNS) for the test cases considered in this paper.

High order WENO finite difference scheme with adaptive dual order ideal weights for hyperbolic conservation laws

An adaptive even order weighted essentially non-oscillatory polynomial reconstruction procedure (WPR) with Z-type weights (WENO-Za) is proposed to reduce the numerical dissipation and improve the resolution of the fine-scale structures in a long-time simulation of the hyperbolic conservation laws. The new spatial solver combines the even and odd order (even order plus one) WENO finite difference schemes together. The novel WENO-Za scheme adapts the ideal weights, instead of the nonlinear weights, between the even and odd order based on a nonlinear transition function, which is a function of the odd order global smoothness indicator and a user-adjustable parameter. The dissipation and dispersion behaviors of the WENO-Za scheme is illustrated by the approximate dispersion relation technique. For the Euler equations, the WPR procedure is performed on each positive and negative split flux variable in the characteristic space. The performance of the WENO-Za scheme, in terms of resolution, essentially non-oscillatory shock-capturing, and efficiency, are evaluated by solving several benchmark shock-tube problems, such as the extended shock-entropy interaction problem, the extended shock-density interaction problem, the two blast-waves interaction problem, the Riemann problem, and the forward-facing step problem. The results show that the WENO-Za scheme can 1) retain the fine-scale structures in the smooth regions better due to the reduction of numerical dissipation of the even order scheme in exchange for a slightly larger dispersive error in a long-time simulation and 2) capture localized strong gradients and shocks in an essentially non-oscillatory manner due to the strong sub-stencil biasing in the odd order scheme. The space-time evolutions of the transition functions demonstrate the robust adaptive nature of the WENO-Z4a5 scheme in the regions of shock, contact discontinuity, and rarefaction waves.

Semi-Automatic Image Processing System of Aeromagnetic Data for Structural and Mining Investigations (Case of Bou Azzer Inlier, Central Anti-Atlas, Morocco)

Numerical analysis of geophysical data to uncover Precambrian belts and probably to enclose mineral deposits is becoming once more communal in mining activity. The method is founded on typifying zones branded to comprehend deposits and looking for analogous areas. The proposed work outlines a semi-automatic image processing system for the structural and mining investigation of the Bou Azzer inlier, which varies from preceding approaches as it is centered only on aeromagnetic data. The aeromagnetic signature of what seem to be geologically expressive features are pursued within the aeromagnetic items. Cobalt and associated mineralizations in the Bou Azzer inlier are recognized to arise nearby main crustal discontinuities revealing as significant shear zones, which turn act as drains for mineralizing fluids. Mineralization occurs in sectors of structural complexity beside the shear zones. Developing towards the semi-automatic uncovering of such regions, the furthermost prospective extents are those everywhere inferred structural complexity occurs next to the regions of magnetic discontinuity. The proposed method is mainly based on the approach developed by the center for exploration targeting. The study was led by means of aeromagnetic data from the Bou Azzer inlier, which is considered one of the most productive and prospective regions for minerals and base metal mineralization in Morocco. The combined results obtained from geological and geophysical data prove that prospective areas have a dominant trend of NNE-SSW, NW-SE, NNW-SSE, E-W, and NE-SW directions. The CET Grid and Porphyry Analyses show that the probable porphyry mineral deposit locations mainly concentrated in the center of inlier, the Foum Zguid dyke, and northern and eastern part, which correspond to the Bou Azzer ophiolitic complex and platform deposits of the Lower Neoproterozoic Tachdamt-Bleïda.

Evaluation of the Bond Stress Transfer Mechanism in CFSTs

This paper studies the non-linear distribution of bond–slip behavior in the steel concrete interface of a Concrete Filled Steel Tube (CFST). Specifically, it concerns the regions of geometric discontinuity occurring in composite beams of CFST column-frame connection points. The study was conducted through an analytical model that represented the bond stress transfer mechanism within these areas. The resulting deductions were drawn up on the basis of the elasticity theory and the non-linear bond–slip relationship between the steel jacket and the confined concrete. This paper highlights how the model proposed here was able to obtain, not only the closed-form analytical expression of the transferring length involved in the bond stress transfer mechanism in CFSTs but also the expressions of concrete and steel jacket stresses and strains. In addition, the procedure also obtained the bond stress and slip trend in the above-mentioned length for rectangular and circular concrete filled steel tubes. The use of this model also resulted in an analytical expression for the calculation of the ultimate load in CFSTs. In this paper, the ultimate load predictions were compared with the experimental results obtained from 97 tests carried out on circular concrete filled tubes (CCFTs) and 35 tests on rectangular concrete filled tubes (RCFTs). The predictions drawn up with this model have been found to be the most accurate and uniform in comparison with those obtained from models proposed by other authors and Eurocode. With reference to the experimental-to-analytical load value ratio, the AVG and COV values obtained from the model proposed here are 0.86 and 0.42, and 1.06 and 0.57 for CCFT and RCFT analyses, respectively.

Numerical simulation of merging of two rising bubbles with different densities and diameters using an enhanced Volume-Of-Fluid (VOF) model

In this study, the transient evolution of two rising bubbles with different densities is investigated numerically using an enhanced version of the VOF model, aiming to establish an state-of-the-art benchmark solutions and up-to-date data set for CFD validations. The simulations are performed on the staggered grid system where a novel third‐order accurate monotone convection scheme is applied for the discretization of the convection terms in Navier-Stokes and volume fraction equations while the semi-iterative PISOC algorithm (a combined version of the classical PISO and Chorin's model) are used to solve the pressure-velocity coupling. To reduce the false diffusion errors and mitigate smearing of interface thickness in the regions of physical discontinuities, the interface compression technique is also incorporated into the transport equation. To further enhance the accuracy of the numerical solutions, the idea of Piecewise Linear Interface Calculation (PLIC) based on the ELVIRA technique (Efficient Least-square Volume-of-fluid Interface Reconstruction Algorithm) is also utilized for the interface reconstruction and accurate implementation of surface tension force. The validity and accuracy of the enhanced VOF model is further demonstrated against a series of challenging benchmark cases including draining of liquids from the storage tank (tank draining), single rising bubble, three-phase Rayleigh-Taylor Instability and dam-break flows over dry and wet beds. The comparison of the obtained results with previously published data vividly demonstrates the superiority of the proposed method over the standard VOF/Level-Set models in handling multiphase/multi-fluid flow problems with large topological changes. In the last stage, the morphology and hydrodynamic characteristics of merging of two rising bubbles with different densities and diameters are examined and analyzed in details. The results show that, the initial/final deformations and the subsequent steady-state rise of two bubbles are remarkably influenced by the diameters of leading (upper) and trailing (lower) bubbles.

Reinforcing of discontinuity regions in concrete deep beams with GFRP composite bars

The behavior of concrete deep beams internally-reinforced with glass fiber-reinforced polymer (GFRP) bars around regions of discontinuity is investigated. Twelve deep beam specimens were tested. One specimen was solid whereas the remaining eleven specimens included an opening in the shear span. Test variables included the opening height, concrete grade, and GFRP reinforcing configuration around the discontinuity regions. Three different GFRP reinforcing schemes around the discontinuity regions were employed. The scheme with diagonal GFRP reinforcement crossing the bottom chord was more effective in improving the shear resistance than that having diagonal GFRP reinforcement crossing the top chord. The strength gain caused by the GFRP reinforcement was more significant for the deep beams with the greater opening height. In contrast, increasing the opening height reduced the strength enhancement caused by increasing the concrete grade. Test results were compared to the strut-and-tie modeling (STM) predictions. The STM tended to provide reasonable predictions for the nominal shear strength of the beams reinforced with GFRP bars around the discontinuity regions. Provisions of the Canadian Standards Association provided more conservative predictions for the nominal strength compared with those provided by provisions of the American Concrete Institute.

Rp‐adaptation for compressible flows

AbstractWe present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature‐based sensors or error estimators. We demonstrate this proof‐of‐concept using two geometries in transonic and supersonic flow regimes. The method has been implemented in the open‐source spectral/hp element framework Nektar++, and adaptivity is performed by its dedicated high‐order mesh generation tool NekMesh. The results show that the proposed rp‐adaptation methodology is a reasonably cost‐effective way of improving simulation accuracy.

Pharmacophore modeling of JAK1: A target infested with activity-cliffs

Janus kinase 1 (JAK1) is protein kinase involved in autoimmune diseases (AIDs). JAK1 inhibitors have shown promising results in treating AIDs. JAK1 inhibitors are known to exhibit regions of SAR discontinuity or activity cliffs (ACs). ACs represent fundamental challenge to successful QSAR/pharmacophore modeling because QSAR modeling rely on the basic premise that activity is a smooth continuous function of structure. We propose that ACs exist because active ACs members exhibit subtle, albeit critical, enthalpic features absent from their inactive twins. In this context we compared the performances of two computational modeling workflows in extracting valid pharmacophores from 151 diverse JAK1 inhibitors that include ACs: QSAR-guided pharmacophore selection versus docking-based comparative intermolecular contacts analysis (db-CICA). The two methods were judged based on the receiver operating characteristic (ROC) curves of their corresponding pharmacophore models and their abilities to distinguish active members among established JAK1 ACs. db-CICA modeling significantly outperformed ligand-based pharmacophore modeling. The resulting optimal db-CICA pharmacophore was used as virtual search query to scan the National Cancer Institute (NCI) database for novel JAK1 inhibitory leads. The most active hit showed IC50 of 1.04 μM. This study proposes the use of db-CICA modeling as means to extract valid pharmacophores from SAR data infested with ACs.

Observation of quantum signature in rivastigmine chemical bond break-up and quantum energetics, spectral studies of anti-Alzheimer inhibitors

Semi-empirical calculations on the torsion potential for dihedral angle of rivastigmine linking NAP and Carbamyle moieties consistently show regions of several discontinuities and a cusp indicating molecular instability and eventual break-up of rivastigmine observed in the X-ray structure. The phenomena can be explained both by definition of large classical force or quantum nature of chemical bond break-up. Also, to better understand the molecular properties and quantum energetics of the inhibitor molecules, we have performed several ab initio based calculations on all four inhibitors at equilibrium geometry, in ground state and gas phase using the density functional theory level wB97X/6-31G* and HF/6-31G*. A number of properties like computational vibrational (IR), Raman and nuclear magnetic resonance (NMR) spectra as well as HOMO and LUMO orbital energies at optimized geometries have been computed by SPARTAN16 and Gaussian16 utilities. Also, the thermodynamic and QSAR properties of the inhibitors have been assessed and compared by a number of different semi-quantum, Hartree-Fock and density functional methods. The theoretical NMR and IR spectra have been benchmarked against experimental spectrum to compare and assess suitability of the computational methodologies and basis set levels for the calculations.Communicated by Ramaswamy H. Sarma

Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model

Abstract The kinetic flux vector splitting method has been introduced for two-dimensional system of shallow water equations with horizontal temperature gradients. The scheme preserves positivity conditions and resolves different regions of shock waves, rarefaction waves and contact discontinuity with negligible oscillations. The scheme is based on splitting of flux functions of the Ripa model. Moreover Runge-Kutta time stepping technique with MUSCL-type initial reconstruction is used to guarantee higher order accurate solution. The numerical example is taken from already published article. The obtained results reveal the accuracy and robustness of the proposed method.

Analysis of a high-order finite difference detector for discontinuities

ABSTRACTHigh-order finite difference discontinuity detectors are essential for the location of discontinuities on discretized functions, especially in the application of high-order numerical methods for high-speed compressible flows for shock detection. The detectors are used mainly for switching between numerical schemes in regions of discontinuity to include artificial dissipation and avoid spurious oscillations. In this work a discontinuity detector is analysed by the construction of a piecewise polynomial function that incorporates jump discontinuities present on the function or its derivatives (up to third order) and the discussion on the selection of a cut-off value required by the detector. The detector function is also compared with other discontinuity detectors through numerical examples.

Fringe filtering technique based on local signal reconstruction using noise subspace inflation

A noise filtering technique is proposed to filter the fringe pattern recorded in the optical measurement set-up. A single fringe pattern carrying the information on the measurand is treated as a data matrix which can either be complex or real valued. In the first approach, the noise filtering is performed pixel-wise in a windowed data segment generated around each pixel. The singular value decomposition of an enhanced form of this data segment is performed to extract the signal component from a noisy background. This enhancement of matrix has an effect of noise subspace inflation which accommodates maximum amount of noise. In another computationally efficient approach, the data matrix is divided into number of small-sized blocks and filtering is performed block-wise based on the similar noise subspace inflation method. The proposed method has an important ability to identify the spatially varying fringe density and regions of phase discontinuities. The performance of the proposed method is validated with numerical and experimental results.

Continuous-switch piecewise quadratic models of biological networks: Application to bacterial growth

An extension of the class of piecewise linear (PL) systems is proposed to model gene expression dynamics dependent on dilution due to cell growth rate. The growth rate is modeled as the weighted minimum of two or more limiting gene products responsible for bacterial growth. The production terms are still piecewise constant, but now the degradation terms are piecewise quadratic (PQ). This new mathematical formalism exhibits continuous switches between PQ modes. We first study the novel dynamical behavior generated by the nonlinear terms at the regions of discontinuity of the vector fields, showing that the sliding motion configurations occurring in PL systems can further lead to damped convergent oscillations or periodic behavior in PQ systems. As an application, a core model of the bacterial gene expression machinery is studied with the goal of externally tuning the growth rate of cells. This system may exhibit several behaviors including bi-mode bistability or damped oscillatory behavior.

Magnetic resonance temperature imaging-based quantification of blood flow-related energy losses.

This study presents a new approach for evaluating bioheat transfer equation (BHTE) models used in treatment planning, control and evaluation of all thermal therapies. First, 3D magnetic resonance temperature imaging (MRTI) data are used to quantify blood flow-related energy losses, including the effects of perfusion and convection. Second, this information is used to calculate parameters of a BHTE model: in this paper the widely used Pennes BHTE. As a self-consistency check, the BHTE parameters are utilized to predict the temperatures from which they were initially derived. The approach is evaluated with finite-difference simulations and implemented experimentally with focused ultrasound heating of an ex vivo porcine kidney perfused at 0, 20 and 40 ml/min (n = 4 each). The simulation results demonstrate accurate quantification of blood flow-related energy losses, except in regions of sharp blood flow discontinuities, where the transitions are spatially smoothed. The smoothed transitions propagate into estimates of the Pennes perfusion parameter but have limited effect on the accuracy of temperature predictions using these estimates. Longer acquisition time periods mitigate the effects of MRTI noise, but worsen the effect of flow discontinuities. For the no-flow kidney experiments the estimates of a uniform, constant Pennes perfusion parameter are approximately zero, and at 20 and 40 ml/min the average estimates increase with flow rate to 3.0 and 4.2 kg/m(3) /s, respectively. When Pennes perfusion parameter values are allowed to vary spatially, but remain temporally constant, BHTE temperature predictions are more accurate than when using spatially uniform, constant Pennes perfusion values, with reductions in RMSE values of up to 79%. Locations with large estimated perfusion values correspond to high flow regions of the kidney observed in T1 -weighted MR images. This novel, MRTI-based technique holds promise for improving understanding of thermal therapy biophysics and for evaluating biothermal models.

Systematic artifacts in support vector regression-based compound potency prediction revealed by statistical and activity landscape analysis.

Support vector machines are a popular machine learning method for many classification tasks in biology and chemistry. In addition, the support vector regression (SVR) variant is widely used for numerical property predictions. In chemoinformatics and pharmaceutical research, SVR has become the probably most popular approach for modeling of non-linear structure-activity relationships (SARs) and predicting compound potency values. Herein, we have systematically generated and analyzed SVR prediction models for a variety of compound data sets with different SAR characteristics. Although these SVR models were accurate on the basis of global prediction statistics and not prone to overfitting, they were found to consistently mispredict highly potent compounds. Hence, in regions of local SAR discontinuity, SVR prediction models displayed clear limitations. Compared to observed activity landscapes of compound data sets, landscapes generated on the basis of SVR potency predictions were partly flattened and activity cliff information was lost. Taken together, these findings have implications for practical SVR applications. In particular, prospective SVR-based potency predictions should be considered with caution because artificially low predictions are very likely for highly potent candidate compounds, the most important prediction targets.

Do subglottal resonances lead to quantal effects resulting in the features [back] and [low]?: A review

A question of general interest is why languages have the sound categories that they do. K. N. Stevens proposed the Quantal Theory of phonological contrasts, suggesting that regions of discontinuity in the articulatory-acoustic mapping serve as category boundaries. H. M. Hanson and K. N. Stevens [Proc. ICPhS, 182–185, 1995] modeled the interaction of subglottal resonances with the vocal-tract filter, showing that when a changing supraglottal formant strays into the territory of a stationary tracheal formant, a discontinuity in supraglottal formant frequency and attenuation of the formant peak occurs. They suggested that vowel space and quality could thus be affected. K. N. Stevens [Acoustic Phonetics, MIT Press, 1998] went further, musing that because the first and second subglottal resonances lead to instabilities in supraglottal formant frequency and amplitude, vowel systems would benefit by avoiding vowels with formants at these frequencies. Avoiding the first subglottal resonance would naturally lead to the division of vowels into those with a low vs. non-low tongue body; avoiding the second would lead to the division of vowels into those having a back vs. front tongue body. We will review subsequent research that offers substantial support for this hypothesis, justifying inclusion of the effects of subglottal resonances in phonological models.

A Method to Approximate the Steady-State Creep Response of Three-Dimensional Pipe Bend Finite Element Models Under Internal Pressure Loading Using Two-Dimensional Axisymmetric Models

Pipe bends are regions of geometric discontinuities in the pipe systems used in power plants and most industry recorded failures have been located around similar regions. Understanding these potential locations of weakness is therefore of great interest for the safe and economic operation of piping components. Increased predictive accuracy would assist in component design, condition monitoring, and retirement strategy decisions. Modeling of piping components for finite element analysis (FEA) is complicated by the variation of the cross section dimensions (changes in wall thicknesses or cross section ovality) around the pipe bend due to the manufacturing procedure implemented. Quantities such as peak rupture stress and creep rupture life can be greatly affected by these geometric variation (Rouse, J. P., Leom, M. Z., Sun, W., Hyde, T. H., Morris, A., “Steady-state Creep Peak Rupture Stresses in 90 Pipe Bends with Manufacture Induced Cross Section Dimension Variations”International Journal of Pressure Vessels and Piping, Volumes 105–106, May–June 2013, pp. 1–11). Three dimensional (3D) models can be used to approximate to the realistic level of detail found in pipe bends. These simulations may however be computationally expensive and could take a considerable amount of time to complete. Two dimensional (2D) axisymmetric models are relatively straight forward to produce and quick to run, but of course cannot represent the full geometric complexity around the pipe bend. A method is proposed that utilises multiple 2D axisymmetric pipe bend models to approximate the result of a 3D analysis through interpolation, thus exploiting the greatly reduced computing time observed for the 2D models. The prediction of peak rupture stress (both magnitude and location) is assessed using a simple power law material model. Comments are made on the applicability of the proposed procedure to a range of bends angles (90 deg, 60 deg, and 30 deg), as well as the effect of the stress exponent (n) and tri-axial (α) material constants. Provided that peak stresses do not occur at the bend/straight interface, the magnitude and location of the peak rupture stress can be predicted by the 2D axisymmetric interpolation method with a typical percentage difference of less than 1%.

Origins of thek−2spectrum in decaying Taylor-Green magnetohydrodynamic turbulent flows

We investigate the origins of k(-2) spectrum in a decaying Taylor-Green magnetohydrodynamic flow with zero large scale magnetic flux that was reported by Lee et al. [Phys. Rev. E 81, 016318 (2010)]. So far, a possible candidate for this scaling exponent has been the weak turbulence phenomenology. From our numerical simulations, we observe that current sheets in the magnetic Taylor-Green flow are formed in regions of magnetic discontinuities. Based on this observation and by studying the influence of the current sheets on the energy spectrum, using a filtering technique, we argue that the discontinuities are responsible for the -2 power law scaling of the energy spectra of this flow.

Divergence-free-preserving high-order schemes for magnetohydrodynamics: An artificial magnetic resistivity method

This paper proposes a new strategy that is very simple, divergence-free, high-order accurate, yet has an effective discontinuous-capturing capability for simulating compressible magnetohydrodynamics (MHD). The new strategy is to construct artificial diffusion terms in a physically-consistent manner, such that the artificial terms act as a diffusion term only in the curl of magnetic field to capture numerical discontinuities in the magnetic field while not affecting the divergence field (thus maintaining divergence-free constraint). The physically-consistent artificial diffusion terms are built into the induction equations in a conservation law form at a partial-differential-equation level. The proposed method may be viewed as adding an artificial magnetic resistivity to the induction equations, and is inherently divergence-free both ideal and resistive MHD, with and without shock waves, and also both inviscid and viscous flows. The method is based on finite difference method with co-located variable arrangement, and we show that any linear finite difference scheme in an arbitrary order of accuracy can be used to discretize the modified governing equations to ensures the divergence-free and the global conservation constraints numerically at the discretization level. The artificial magnetic resistivity is designed to localize automatically in regions of discontinuity in the curl of magnetic field and vanish wherever the flow is sufficiently smooth with respect to the grid scale, thereby maintaining the desirable high-order accuracy of the employed discretization scheme in smooth regions. Two-dimensional smooth and non-smooth ideal MHD problems are considered to validate the capability of the proposed method.