Numerical Phenomena Research Articles

Crucial impact of component Allee effect in predator-prey system

Allee effect in models in interacting species of predator prey system has great significance in ecological context. Allee effect plays crucial role in population dynamics in ecology, where it is the challenging fact that per capita population growth rate is positively dependent on the population density of a species. In this paper, we inspect the famous Hastings and Powell (HP) (Hastings and Powell 1991 Ecology 72 896–903) model incorporating component Allee effect on top predator’s reproduction. We analyse the updated model with the help of both analytical and numerical phenomena. Considering cost of Allee effect, half-saturation constant of prey as the key parameters, the Hopf bifurcations are also analysed. The directions of Hopf bifurcations at the critical values of Allee parameter and half-saturation constant of prey are studied theoretically by using normal form theory introduced by Hassard et al (1981 Theory and Applications of Hopf Bifurcation vol 41 (CUP Archive)). The formulated model indicates that the system demonstrates chaotic, periodic and stable dynamics in the variation of key parameters. The chaos can be controlled for proper application of the large values of parameter used as the cost of Allee effect and also for small values of the parameter used as the half saturation constant of prey population. The results of this study are applicable in the field of marine and wild ecosystem dynamics.

Modal Discontinuous Galerkin Simulations for Grad’s 13 Moment Equations: Application to Riemann Problem in Continuum-Rarefied Flow Regime

For real-world engineering applications, there is a great deal of interest in developing effective models and simulations of continuum-rarefied gas flows. In this study, the numerical simulations of Grad’s 13 (G13) moment equations with application to the Riemann problem in a wide range of continuum-rarefied flow regimes are presented. This work emphasizes numerical robustness and wave phenomena in the G13 system to provide a building block for regularized 13 moment systems, and high-order Grad’s models. For this purpose, a high-order modal discontinuous Galerkin solver is developed for solving one-dimensional G13 moment equations. For spatial discretization, hierarchical modal basis functions premised on orthogonal-scaled Legendre polynomials are used. The proposed approach reduces the G13 systems into a framework of ordinary differential equations in time, which are addressed by an explicit third-order SSP Runge-Kutta algorithm. Three Riemann test cases, including the shock tube, two shock waves and two rarefaction waves, are examined in continuum-rarefied flow regimes. In the G13 system, the arising characteristic waves and dissipation phenomena are investigated in depth. The numerical results demonstrate that every Riemann problem does not have a solution for the G13 system because of loss of hyperbolicity of the system.

Exploring numerical blow-up phenomena for the Keller–Segel–Navier–Stokes equations

Abstract The Keller–Segel–Navier–Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial organism density mass is below 2π there exist globally defined generalised solutions, but what is less understood is whether there are blow-up solutions beyond such a threshold and its optimality. Motivated by this issue, a numerical blow-up scenario is investigated. Approximate solutions computed via a stabilised finite element method founded on a shock capturing technique are such that they satisfy a priori bounds as well as lower and L 1(Ω) bounds for the organism and chemoattractant densities. In particular, these latter properties are essential in detecting numerical blow-up configurations, since the non-satisfaction of these two requirements might trigger numerical oscillations leading to non-realistic finite-time collapses into persistent Dirac-type measures. Our findings show that the existence threshold value 2π encountered for the organism density mass may not be optimal and hence it is conjectured that the critical threshold value 4π may be inherited from the fluid-free Keller–Segel equations. Additionally it is observed that the formation of singular points can be neglected if the fluid flow is intensified.

Exploring Stability and Accuracy Limits of Distributed Real-Time Power System Simulations via System-of-Systems Cosimulation

Electromagnetic transients (EMT) is the most accurate, but computationally expensive method of analyzing power system phenomena. Thereby, interconnecting several real-time simulators can unlock scalability and system coverage, but leads to a number of new challenges, mainly in time synchronization, numerical stability, and accuracy quantification. This study presents such a cosimulation, based on digital real-time simulators (DRTS), connected via Aurora 8B/10B protocol. Such a setup allows to analyze complex and hybrid system-of-systems whose resulting numerical phenomena and artifacts have been poorly investigated and understood so far. We experimentally investigate the impact of IEEE 1588 precision time protocol synchronization assessing both time and frequency domains. The analysis of the experimental results is encouraging and show that numerical stability can be maintained even with complex system setups. Growing shares of inverter-based renewable power generation require larger and interconnected EMT system studies. This work helps to understand the phenomena connected to such DRTS advanced cosimulation setups.

Ground-penetrating radar wavefield simulation via physics-informed neural network solver

The traditional methods for ground-penetrating radar (GPR) wavefield simulation suffer from numerical dispersion phenomena and difficulties for models with complex geometry. We propose to use the physics-informed neural networks (PINNs) to solve the GPR wave equation and model the wavefield propagation. Deep fully connected networks are used to approximate the solution to the equations. Automatic differentiation with back propagation is taken to calculate the partial derivatives. The loss function combining the wave equation, boundary condition, and temporal constraints is constructed and minimized to train the PINNs. As the solver is mesh-free, this simulation method avoids numerical dispersion artifacts and is very flexible in implementation for inversion. The numerical examples indicate that the PINNs solver for GPR wavefield simulation has high accuracy and efficiency. We also explore the possibility of inverting the electrical parameters from the observed wavefields. The results demonstrate the promising potential of the proposed approach in GPR forward modeling.

Study of the impact of the Îlot Tison weir on bedload transport of the Clain River (Poitiers, France) using BASEMENT software

AbstractAn increasing number of numerical morphodynamic models predict the evolution of bed configuration over a wide spectrum of spatial and temporal scales due to the development of advanced numerical methods and increased computational power. The increasing use of numerical morphodynamic models is closely related to the growing availability of high‐resolution river data sets. Today, the main difficulty in using numerical morphodynamic models is that they are used by nonspecialists modellers or modellers that are not morphodynamics specialists, which can lead to errors. These errors include inadequate parameterization of processes for applications at larger spatial and temporal scales, confusion between physical and numerical phenomena when interpreting numerical results, and the assumption that there is a need for a huge volume of data for developing numerical morphodynamic models. The present work aims to achieve two objectives. To avoid these errors, the first objective is to outline the steps in the development of numerical morphodynamic models. The development of numerical morphodynamic models is now possible with public databases. The second objective is to show the effectiveness of BASEMENT to study the impact of existing and future structures on the river hydrodynamics and bedload transport using case study examples.

Galerkin neural network approximation of singularly-perturbed elliptic systems

We consider the neural network approximation of systems of partial differential equations exhibiting multiscale features such as the Reissner–Mindlin plate model which poses significant challenges due to the presence of boundary layers and numerical phenomena such as locking. This work builds on the basic Galerkin Neural Network approach established in Ainsworth and Dong (2021) for symmetric, positive-definite problems. The key contributions of this work are (1) the analysis and comparison of several new least squares-type variational formulations for the Reissner–Mindlin plate, and (2) their numerical approximation using the Galerkin Neural Network approach. Numerical examples are presented which demonstrate the ability of the approach to resolve multiscale phenomena such for the Reissner–Mindlin plate model for which we develop a new family of benchmark solutions which exhibit boundary layers.

Modeling and analysis of water vapor dynamics in high-temperature proton exchange membrane fuel cell coupling gas-crossover phenomena

A 3-D numerical model coupling gas-crossover phenomena for high-temperature proton exchange membrane fuel cell (HT-PEMFC) is developed to investigate the water vapor behavior. After model validation, sensitivity analysis of the water vapor diffusion coefficient is carried out, which does not further affect the water vapor behavior, when the order of magnitude of diffusion coefficient is higher than 10−5m2/s. It is also found that the water vapor transport flux decreases with increasing membrane thickness. However, the flux increases slightly with increasing the catalyst layer. In addition, Increasing the pressure and humidity on the anode side will cause water vapor to diffuse from the anode to the cathode, while increasing the current density or the pressure of cathode, the rate of water vapor transport from the cathode to the anode is enhanced. In the dead-end mode, the accumulation of water vapor at the anode outlet is the main cause for the reversible performance decline, which can be restored through reasonable purge strategies. This work contributes to improve the water management strategy of HT-PEMFC operating in dead-end mode.

Identification of swelling/shrinking coefficients under CO2 on an FKM O-ring – Comparison with HNBR and influence of reinforcements on the matrices

A better understanding of elastomers’ behavior during Rapid Gas Decompression (RGD) requires advanced knowledge of what is happening during gas sorption and desorption. This will offer to improve numerical simulation phenomena to consider a real environmental use of an O-ring, as for thermal applications. A previous experimental study developed testing protocols to investigate the performance of elastomeric O-rings. The non-contact measurement technique has been validated to identify the swelling and shrinking coefficients during sorption and desorption of carbon dioxide (CO2) from a Hydrogenated Nitrile Butadiene Rubber (HNBR) O-ring. The present work describes the effect of CO2 pressures on Fluorocarbon rubber (FKM) seals behavior coupled with temperature. To evaluate the effect of reinforcing the HNBR and FKM matrices with nanofillers, experimental tests were carried out and compared with those of the two elastomers without fillers. The four materials’ CO2 sorption and desorption coefficients are identified, and their swelling upon decompression is measured. It appears that HNBR is the best candidate under the applied service conditions. On the other hand, the nanofillers introduced in the elastomers may cause some early damages under RGD conditions.

Residual stress constrained self-support topology optimization for metal additive manufacturing

This paper proposes a topology optimization method to design self-support structures for metal additive manufacturing. Constraining the process-induced residual stresses is considered with this method to avoid part failures of cracking, delamination, or warpage. Specifically, an inherent strain method-based finite element analysis model is presented to simulate the complex mechanical behavior during the additive manufacturing process. Then, according to the inherent strain-based fast simulation model, the residual stress constrained self-support topology optimization algorithm is formulated, and more importantly, the critical sensitivity information is derived through the adjoint analysis and validated with the finite difference method. Finally, the proposed method is applied to several 2D benchmark examples to demonstrate the effectiveness on residual stress and distortion control. The influences of different RAMP interpolation parameters, residual stress upper limits, and printing directions on the residual stress-constrained design effect are thoroughly explored. A comprehensive discussion is presented at the end to summarize the numerical phenomena.

Is Computational Oceanography Coming of Age?

AbstractComputational oceanography is the study of ocean phenomena by numerical simulation, especially dynamical and physical phenomena. Progress in information technology has driven exponential growth in the number of global ocean observations and the fidelity of numerical simulations of the ocean in the past few decades. The growth has been exponentially faster for ocean simulations, however. We argue that this faster growth is shifting the importance of field measurements and numerical simulations for oceanographic research. It is leading to the maturation of computational oceanography as a branch of marine science on par with observational oceanography. One implication is that ultraresolved ocean simulations are only loosely constrained by observations. Another implication is that barriers to analyzing the output of such simulations should be removed. Although some specific limits and challenges exist, many opportunities are identified for the future of computational oceanography. Most important is the prospect of hybrid computational and observational approaches to advance understanding of the ocean.

Wetting dynamics of a sessile ferrofluid droplet on solid substrates with different wettabilities

There are several numerical approaches to define a permanent magnet in terms of mathematical equations, and each approach has progressed since its inception, but still endures some limitations on specific numerical phenomena. This study seeks to propose a novel numerical representation of a permanent magnet without incorporating its effect through boundary conditions, which overcomes the limitations of previous studies and enables us to introduce a magnetic field of desired strength at any location. A self-correcting method is modified to incorporate the magnetic field effects, while a simplified lattice Boltzmann method is utilized to solve the governing equations for flow field and interface. The validity of the proposed method is ensured by simulating some benchmark phenomena with and without the external magnetic field. This study also investigates the wetting dynamics of a sessile ferrofluid droplet deposited on solid substrates with different wettabilities. The influence of uniform and non-uniform magnetic fields on droplet spreading is discussed in detail. It is observed that for a non-uniform magnetic field in vertical direction, the ferrofluid droplet on a hydrophilic surface does not observe the spherical cap approximation unless the magnetic field strength is below saturation magnetization. Moreover, if the magnet is located above, the droplet undergoes large deformations and achieves pointy shapes with sharp tips on less wettable surfaces.

Hopf Bifurcation of a Gene-Protein Network Module with Reaction Diffusion and Delay Effects

The infinite dimensional partial delay differential equation is set forth and delay difference state feedback control is considered to describe the cell cycle growth in eukaryotic cell cycles. Hopf bifurcation occurs as varying free parameters and time delay continuously and the multi-layer oscillation phenomena of the homogeneous steady state of a simple gene-protein network module is investigated. Normal form is derived based on normal formal analysis technique combined with center manifold theory, which is further to compute the bifurcating direction and the stability of bifurcation periodical solutions underlying Hopf bifurcation. Finally, the numerical simulation oscillation phenomena is in coincidence with the theoretical analysis results.

Topological constraints in 2D structural topology optimization

One of the straightforward definitions of structural topology optimization is to design the optimal distribution of the holes and the detailed shape of each hole implicitly in a fixed discretized design domain. However, typical numerical instability phenomena of topology optimization, such as the checkerboard pattern and mesh dependence, all take the form of an unexpected number of holes in the optimal result in standard density-type design methods, such as SIMP and ESO. Typically, the number of holes is indirectly controlled by tuning the value of the radius of the filter operator during the optimization procedure, in which the choice of the value of the filter radius is one of the most opaque and confusing issues for a beginner unfamiliar with the structural topology optimization algorithm. Based on the soft-kill bi-directional evolutionary structural optimization (BESO) method, an optimization model is proposed in this paper in which the allowed maximal number of holes in the designed structure is explicitly specified as an additional design constraint. The digital Gauss-Bonnet formula is used to count the number of holes in the whole structure in each optimization iteration. A hole-filling method (HFM) is also proposed in this paper to control the existence of holes in the optimal structure. Several 2D numerical examples illustrate that the proposed method cannot only limit the maximum number of holes in the optimal structure throughout the whole optimization procedure but also mitigate the phenomena of the checkerboard pattern and mesh dependence. The proposed method is expected to provide designers with a new way to tangibly manage the optimization procedure and achieve better control of the topological characteristics of the optimal results.

Understanding and investigating the relationships between geometrical errors and lost particles in MCNP

Abstract Generating Constructive Solid Geometry (CSG) ready for MCNP input using automated programs, and the use of universe structures, may give raise to geometrical inconsistencies leading to numerical phenomena known as lost particles, which perturb the statistical reliability of the transport solution. In the context of the reference nuclear analysis models developed for ITER, there is a need to better understand these phenomena, define a sufficiently explicit way to test the models, and provide clear and uniform parameters indicating their technical quality and reliability in terms of geometrical errors. Using a source able to generate an isotropic and uniform fluence inside its closed surface, it was possible to derive a relationship between source’s surface area, lost particles rate and error size. These results were verified with multiple MCNP runs and good agreement was found between simulations results and analytical predictions. This work allows defining more explicit and uniform procedures to debug for lost particles, and provides a way to grade model quality based on objective parameters, like the size of errors, instead of using others that heavily depend on the setup on which the simulation was run.

Quasi-periodic oscillations in the system of three coupled van der Pol oscillators

In this paper, we discuss quasi-periodic oscillations in the system of three dissipatively coupled van der Pol oscillators by the KAM method. In order to use this method, we apply the idea of the averaging method to the original system and obtain some normal form in which the frequency map satisfies a weaker nondegeneracy condition instead of the usual one. Then, it is proved that the system has quasi-periodic invariant 3-tori for most of the parameter set where its averaged system possesses invariant 3-tori. Our result verifies some numerical phenomena of Emelianova et al. (2013, 2014).

How accurate are finite elements on anisotropic triangulations in the maximum norm?

In Kopteva (2014) a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order pointwise accurate. This example was given in the context of a singularly perturbed reaction–diffusion equation. In this paper, we present further examples of unanticipated pointwise convergence behaviour of Lagrange finite elements on anisotropic triangulations. In particular, we show that linear finite elements may exhibit lower than expected orders of convergence for the Laplace equation, as well as for certain singular equations, and their accuracy depends not only on the linear interpolation error, but also on the mesh topology. Furthermore, we demonstrate that pointwise convergence rates which are worse than one might expect are also observed when higher-order finite elements are employed on anisotropic meshes. A theoretical justification will be given for some of the observed numerical phenomena.

Influence of Complex Promoter Structure on Gene Expression

A gene is often regulated by a variety of transcription factors, leading to complex promoter structure. However, how this structure affects gene expression remains elusive. Here, this paper studies a stochastic gene model with the promoter containing arbitrarily many active and inactive states. First, the authors use the binomial moment method to derive analytical steady-state distributions of the mRNA and protein numbers. Then, the authors analytically investigate how the promoter structure impacts the mean expression levels and the expression noise. Third, numerical simulation finds interesting phenomena, e.g., the common on-off model overestimates the expression noise in contrast to multiple-state models; the multi-on mechanism can reduce the expression noise more than the multi-off mechanism if the mean expression level is kept the same; and multiple exits of transcription can result in multimodal distributions.

CFD study of the supercritical transesterification of triolein: Wall-to-fluid/particle-to fluid transport effects

Transesterification of triglycerides is a process by which biodiesel is produced. Biodiesel is a sustainable alternative to petroleum diesel; hence, its efficient production is of significant importance. The transesterification of triolein with methanol under supercritical conditions in the presence of a solid catalyst structured as packed beds is of particular interest due to high yields at moderate temperatures and continuous operability. Fundamental understanding of the heat and mass transfer phenomena in a supercritical transesterification reaction is paramount for a better modelling of the reaction.Computational Fluid Dynamics (CFD) were used to study, by means of a simplified numerical model, heat and mass transport phenomena in a supercritical transesterification reactor. The CFD model was built replicating an experimental pilot plant reactor. Simulations were performed for a 3D geometrical model of a packed bed of cylindrical catalysts. Wall-to-fluid and particle-to-fluid heat and mass transfer were studied for a fluid mixture of methanol (CH3OH) and triolein (C57H104O6) along with co-solvent carbon dioxide (CO2), flown into the packed bed under supercritical conditions (25 MPa, 473.15 K). Detailed flow, temperature and concentration profiles in packed bed were obtained. Free and forced convection effects for different flow rates were analyzed. Large density gradients were observed near the packed bed inlet, generating hydrodynamic instabilities due to natural convection as observed in Metais-Eckert maps. Heat and mass transfer coefficients were estimated from CFD data, and the obtained values of Nuw, Nup, Shp were compared against empirical models for different flow rates for validation of the CFD data. The simulation data agreed well with empirical correlationsfor predicting transport coefficients.

Periodic topology optimization of crane boom based on improved soft kill option method

An improved soft kill option (SKO) method is proposed to achieve the optimization design of tower crane boom. For a better optimization performance, a parabolic weight coefficient is suggested and the displacement constraint is taken into consideration. In order to eliminate the numerical instability phenomena like checkerboard and mesh dependence, element temperature filter function is added into SKO method. Through the optimization data comparison of rectangular cantilever plate, it is verified that the improved SKO method can achieve a better result with more uniform stress and higher efficiency. Based on the dimension and load parameters of QTZ63 tower crane boom, an optimization model is established, and a periodic SKO method is put forward to optimize this model. The optimization result of the crane boom can provide a new thought for tower crane boom design.