Time-marching Research Articles

Transient flow modeling in fractured media using graphs.

We describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the O(10^{4}) speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

Simulation investigation of heating rate and temperature uniformity in fluidized bed

In this paper, the hydrodynamics and gas–solid heat transfer characteristics during bed material heating process are investigated using the CFD-DEM approach, and the heating rate and bed temperature uniformity are quantitatively analysed. After model validation, gas–solid heat transfer characteristics in a typical case is analysed. On this basis, the effects of operating conditions is further discussed. The results show that overheating phenomenon at bed bottom is weakened obviously by solid internal circulation behavior in fluidized bed. As time marches, bed temperature uniformity is effectively improved with increasing mean bed temperature. Specially, a temperature drop at particle scale is captured by tracer particle method. A simplified energy balance model is developed to explain the relationship between bulk heating rate and operating conditions, and qualitatively consistent between simulation results and model analytical solutions is captured. Furthermore, the temperature uniformity under different operating conditions is qualitatively discussed by standard deviation of particle temperature.

What Are the Water Sector's Greatest Operations Challenges?

As time and technology march forward, and we experience new challenges like the COVID‐19 pandemic, the world is in a constant state of change. This discussion highlights how operations challenges have changed in the past 20 years, where the water sector stands today, and what the future may hold.

Performance Analysis of Flapping Foil Flow Energy Harvester Mounted on Piezoelectric Transducer using Meshfree Particle Method

Performance of a semi-active flapping foil flow energy harvester, coupled with a piezoelectric transducer has been analyzed in this work. The airfoil is mounted on a spring, damper and piezoelectric transducer arrangement in its translational mode. External excitation is imparted in pitch mode and system is allowed to oscillate in its translational mode as a result of unsteady fluid forces. A piezoelectric transducer is used as an electrical power converter. Flow around moving airfoil surface is solved on a meshfree nodal cloud using Radial Basis Function in Finite Difference Mode (RBF-FD). Fourth order Runge-Kutta Method is used for time marching solution of solid equations. Before the solution of complex Fluid-Structure Interaction problem, a parametric study is proposed to identify the values of kinematic, mechanical and geometric variables which could offer an improved energy harvesting performance. For this purpose, the problem is modelled as a coupled electromechanical system using Lagrange energy equations. Airfoil lift and pitching moment are formulated through Theodorson’s two dimensional thin-plate model and a parametric analysis is conducted to work out the optimized values of pivot location, pitch amplitude, spring stiffness and damping constant. The subsequent computational analysis resulted in an enhanced performance compared to the potential flow model with an efficiency of up to 27% based on total power extraction through the flow. Higher efficiency is obtained when the pitch axis is located aft of mid chord. However, this setting does not correspond to the maximum power output. Interestingly, power is maximized at much lower efficiency values.

A numerical study on the effect of aspect-ratio and density ratio on the dynamics of freely falling plate in the flutter-to-tumble transition regime

The motion of a freely falling thin aluminium plate in water is studied using two-dimensional numerical simulations. The fluid-solid interface is treated using the diffuse interface immersed boundary method. Periodic side-to-side fluttering motion at the small dimensionless moment of inertia $$(I^{*})$$ becomes chaotic in the intermediate range which finally settles for pure tumbling at high $$I^*$$ . Even the stable flutter trajectories exhibit significant sensitivity to incremental deviation in fluid forces brought in by inaccurate time marching. The maximum instantaneous inclination angle of the plate increases with $$I^*$$ during flutter with the uniform multilevel distribution. At larger $$I^*$$ , such distribution collapses to nearly a single level indicating the ability of the plate to autorotate under the influence of turning moment created by the neighbouring fluid. The plate is observed to retain the initial orientation during its flight in the tumbling regime. The range of $$I^{*}$$ for chaotic motion is found to extend with the increase in initial inclination angle. Tests on the effect of initial conditions on the trajectories of the plate indicate while the chaotic regime is mostly affected by initial orientation and velocity of release, flutter and tumble motions converge for a variety of initial states. The chaotic motion transforms into a flutter or tumbles depending on the solid-to-fluid density ratio for a fixed geometry of the plate. However, with a fixed solid-to-fluid density ratio, aspect-ratio of the plate does not alter the stable trajectories appreciably.

On the Thrust Generation from an Elliptic Airfoil in Plunging and Translating Motion at Low Reynolds Numbers

In this paper, numerical simulation elliptic airfoil model, which mimics the biological locomotion, is studied. Elliptic airfoil undergoes a combined plunging and translating at low Reynolds number is simulated by using body fitted coordinate system. The moving mesh in the physical domain is mapped to a regular fixed mesh in the computational domain through a time dependent transformation between the physical and computational co-ordinates. The governing equations of laminar incompressible flow are transformed in the computational plane by incorporating the time dependent transformation, which naturally accounts for the mesh velocities. The transformed equations are discretized on the structured, collocated, o-type elliptic grid using the finite difference methodology. The unsteady equations are marched in time by using a semi-implicit pressure correction (projection) scheme. Along with the time marching of the governing equations, utilizing the mesh velocities and the forward Eulertime integration also moves the mesh points. The effect of Reynolds number (Re) is investigated on the flapping flight propulsion is investigated. It is found that there exists a critical Reynolds number (Rec) for every frequency after which there exists a thrust force. The effect of Rec is related to transformation of neutral wake to thrust generating wake. It is also found that the optimal frequency corresponds to a reduced frequency parameter of 0.7 where a lock in exists. It is also found that this Stc is independent of Re and the mode of vortex shedding is same at Re = 100 and 200 for Stc = 0.7. Further, it is shown that the mode of vortex shedding present is always helpful in thrust generation.

Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump

Abstract The present article revisits the well-known exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump. It studies the stability of exact solutions of semi-linear stochastic pantograph integro differential equations with jump first, gives the conditions which guarantee the existence and uniqueness of an exact solution. Then it constructs exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump and proves that the exponential Euler method is convergent with strong order p = 1 2 . It also studies the stability of the exponential integrators and proves that the exponential Euler method can reproduce the mean-square exponential stability of the analytical solution under some restrictions on the step size. In addition, it presents some numerical experiments to confirm the theoretical results.

A high-order vertex-centered quasi-Lagrangian discontinuous Galerkin method for compressible Euler equations in two-dimensions

This article introduces a new vertex-centered quasi-Lagrangian discontinuous Galerkin method for two-dimensional compressible flows that is third-order accurate both in space and time. The computational domain is divided into structured quadrilateral cells with straight edges. Nodal control volumes with curved edges are constructed surrounding the grid vertices. The Euler equations in arbitrary Lagrangian-Eulerian (ALE) form are discretized on these nodal control volumes using a discontinuous Galerkin method. The time marching is implemented by the third-order strong-stability-preserving Runge-Kutta method. A compact HWENO reconstruction algorithm is used as limiter to eliminate spurious oscillations near discontinuities. The polynomial expression of fluid velocity defined in a nodal control volume is also obtained from the reconstruction procedure, and is used to calculate the moving velocity of corresponding grid vertex. In this way, the grid vertices are moved in a rigorously Lagrangian manner, although there are still mass fluxes between neighbouring nodal control volumes. Therefore the scheme is called as a quasi-Lagrangian one. The scheme is conservative for mass, momentum and total energy. Some numerical tests are carried out to demonstrate the accuracy and robustness of the scheme. It has a favorable qualitative behavior for discontinuous problems and optimal convergence rates for smooth problems.

Convergence and stability of exponential integrators for semi-linear stochastic variable delay integro-differential equations

ABSTRACT In this paper, the numerical method for semi-linear stochastic variable delay integro-differential equations is studied. The stability of analytic solutions of semi-linear stochastic variable delay integro-differential equations are studied first, some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential integrators for semi-linear stochastic variable delay integro-differential equations are constructed, the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with the strong order 1/2 and the exponential Euler method can keep the mean-square exponential stability of the analytical solution under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.

Three-dimensional printing of diamagnetic microparticles in paramagnetic and diamagnetic media

We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

Hospital Expenditure at the End-of-Life: A Time-to-Death Approach.

Background: In recent years the use of time to death (TTD) variables in the modeling of individual health expenditures has been of interest to health economics researchers. The aim of this study was to investigate the effect of age and TTD on hospital inpatient expenditure (HIE). Methods: We used a claims database from Iran Health Insurance Organization of Tehran city that includes considerable proportion of Tehran residents and contains information on insured individuals’ HIE. We included HIE of all insured decedents (30 to 90 years old) who died during March 2013 and March 2014 (n=1018). No sampling was required. According to the decedents’ date of death, we extracted their last 24 months HIE. The period of time March 30, 2011 until March 30, 2014 (3 years) was used to guarantee a full 24 months of observations for decedents. A two-part econometric model was employed to investigate the effect of age, TTD, and some demographic variables on probability and conditional amount of individuals’ hospital expenditure. Stata software (version 16.0) was used for data processing and analysis. Results: Our results demonstrated that the month-based TTDs especially near months before death of decedents (TTD1 to TTD10) significantly affected both probability and conditional amount of HIE. One month before death incurred more HIE than the rest of the months. A further interesting finding is that after including TTD, age variable as a conditional driver of HIE loses its direct effect on decedents’ HIE, but age TTD interaction effect on HIE is still positive and statistically significant. Conclusion: The results confirm that TTD as a proxy of mortality indicator has a considerable effect on decedents’ HIE. The age variable has not directly affected decedents’ HIE but indirectly and through its interaction with TTD has a statistically significant effect on HIE. In addition to age, policy-makers should consider TTD to make better predictions of future HIE.

Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method

This paper is concerned with the delay dependent stability of the stochastic exponential Euler method for stochastic delay differential equations and stochastic delay partial differential equations. By using root locus technique, the necessary and sufficient condition of the numerical delay dependent stability of the method is derived for a class of stochastic delay differential equations and it is shown that the stochastic exponential Euler method can fully preserve the asymptotic mean square stability of the underlying system. Furthermore, we investigate the delay dependent stability of the semidiscrete and fully discrete systems for a linear stochastic delay partial differential equation. The necessary and sufficient condition for the delay dependent stability of the semidiscrete system based on the standard central difference scheme in space is given. Based on this condition, the delay dependent stability of the fully discrete system by using the stochastic exponential Euler method in time is studied. It is shown that the fully discrete scheme can inherit the delay dependent stability of the semidiscrete system completely. At last, some numerical experiments are given to validate our theoretical results.

Stabilized DG-PSTD Method With Nonconformal Meshes for Electromagnetic Waves

We present a node-based discontinuous Galerkin (DG) pseudospectral time domain (PSTD) algorithm, with adaptive nonconformal unstructured meshes, for 3-D large-scale Maxwell’s equations. This algorithm is a combination of a new DG algorithm and a PSTD method, where spectral accuracy is achieved via the PSTD algorithm, while the DG serves as a stable coupling for multiple domains with unstructured hexahedra. Time marching is efficient because the mass matrix in the DG-PSTD algorithm is exactly diagonal. The scheme is low-storage and scalable because the stiffness matrix is localized into a small shared matrix. Furthermore, arbitrary nonconformal meshes can be adaptively realized, increasing the flexibility of complex media modeling. Our numerical results corroborate the long-time stability, high efficiency, and high-order accuracy of the proposed solver. Finally, an adaptive application of 5G electromagnetic signal propagation demonstrates the efficiency and capability of the proposed high-order solver.

Entangled and Estranged: Living and Dying in Relation (to Cancer)

Serious illness has typically been explored as emergent within the relatively linear unfolding of the steady march of time. Here, focusing on cancer and drawing on the accounts of patient/carer dyads, we propose a relational ontology of the affective and temporal entanglements of living-with disease. Emphasising the iterative intra-activity of vital matter and social meaning as they are repatterned across time, we examine the enfolding of various temporal, affective and normative dis/continuities that become particularly meaningful – or are made to matter – in the context of living/dying-with cancer. We focus on the social practices of ‘making memories’, ‘anticipating absence’ and ‘maintaining normal’ which reveal the entanglement of seemingly discrete categories such as self and other, here and gone, and past, present and future. Living-with cancer thus emerges as more than an illness/caring experience, but rather as instructive in contributing to a relational understanding of everyday life.

Rapid Modeling and Simulation of Integrated Circuit Layout in Both Frequency and Time Domains From the Perspective of Inverse

In this article, starting from full-wave partial differential equation (PDE)-based Maxwell’s equations where $\mathbf {E}$ and $\mathbf {H}$ are coupled, we derive a closed-form model of the inverse of Maxwell’s system of equations in the physical layout of an integrated circuit, package, and board. In this model, we decompose the inverse rigorously into $R$ , $C$ , $L$ , and full-wave components, with neither numerical computation nor approximation, and for an arbitrary physical layout. As a result, each component can be found independently and then superposed to obtain the total response of a layout to any circuit stimuli. The time marching and point-by-point frequency sweeping are also avoided for the $RC$ component as this component’s time and frequency dependencies are analytically revealed in the proposed model. Moreover, the full-wave component is efficiently represented by a small number of high-frequency modes. Using the proposed model, not only many accuracy issues related to existing layout modeling can be addressed but also we drastically speed up layout modeling and simulation and provide circuit designers with an effective model for layout automation. In addition, we develop fast and large-scale algorithms to find each component of the inverse rapidly, where many steps are made analytical, thus further saving CPU run time. The proposed work has been applied to large-scale layout extraction and analysis. Superior performance has been demonstrated in accuracy, efficiency, and capacity.

Symmetric Positive Semi-Definite FDTD Subgridding Algorithms in Both Space and Time for Accurate Analysis of Inhomogeneous Problems

In this article, we develop a systematic approach to derive symmetric positive semi-definite (SPD) finite-difference time-domain (FDTD) subgridding operators in both space and time for analyzing general inhomogeneous problems in an accurate fashion. The operators are SPD by construction and independent of the grid ratio. The resultant explicit time marching is guaranteed to be stable because such subgridding operators have only nonnegative real eigenvalues. Furthermore, the use of a time step local to the base grid and the subgrid is permitted without sacrificing stability and accuracy. Moreover, the algorithm takes the subgrid information into account to accurately analyze inhomogeneous problems. In addition, we provide an interpretation of the proposed subgridding operators and show how to implement them in the original difference equation-based FDTD framework. Extensive numerical experiments involving both 2- and 3-D subgrids with various grid ratios and inhomogeneities have demonstrated the stability, accuracy, and efficiency of the proposed new SPD subgridding algorithms.

Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method.

In this research, unsteady three-dimensional incompressible Navier–Stokes equations are solved to simulate experiments with the Boussinesq approximation and validate the proposed numerical model for the design of a circular fin-tube heat exchanger. Unsteady time marching is proposed for a time sweeping analysis of various Rayleigh numbers. The accuracy of the natural convection data of a single horizontal circular tube with the proposed numerical method can be guaranteed when the Rayleigh number based on the tube diameter exceeds 400, which is regarded as the limitation of numerical errors due to instability. Moreover, the effective limit for a circular fin-tube heat exchanger is reached when the Rayleigh number based on the fin gap size () is equal to or exceeds 100. This is because at low Rayleigh numbers, the air gap between the fins is isolated and rarely affected by natural convection of the outer air, where the fluid provides heat resistance. Thus, the fin acts favorably when exceeds 100.

On stability of time marching in numerical solutions of rayleigh-plesset equation for ultrasonic cavitation

Ultrasonic irradiation approach has become one of the most popular methods applied in chemical processing including lignocellulosic biomass pretreatment and industrial cleansing. The phenomenon of ultrasonic cavitation can be indeed delineated via the Rayleigh-Plesset equation (RPE), which governs the transient radius of the bubble. Nonetheless, the time marching in the numerical solutions for RPE is highly unstable, which cannot be assured using von Neumann analysis. High sensitivity of RPE to time step may lead to extremely long computational time. The lack of numerical investigation into the time stepping issue of RPE has hindered in-depth simulation of ultrasonic cavitation. Therefore, the purpose of this paper is to investigate the stability criterion of time stepping for RPE in different time progression schemes, namely Euler explicit, 2nd order Taylor’s method, 4th order Runge-Kutta, Runge-Kutta Fehlberg and Cash-Karp Runge-Kutta method. A simple modified adaptive time step method and α independence study has been introduced in this paper for fast, stable and accurate computation of RPE. Compared with the traditional constant time marching method, the new model is able to improve the computational cost significantly without affecting the time marching stability and resolution of the results. Among the investigated method, Runge-Kutta family solvers have higher computational accuracy, with the cost of higher critical α value. The model is also applied to compute the pressure and temperature hike during bubble collapse due to different sonication power. The simulation results show that the ultrasonic irradiation with higher sonication power could produce a higher energy to break the lignocellulose wall.

Gust Response Computations with Control Surface Freeplay Using Random Input Describing Functions

An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An efficient method to compute the total gust+LCO response is developed using random input describing functions (RIDF), in a manner analogous to harmonic input describing functions for LCO calculation. Results are obtained for an airfoil with trailing edge flap freeplay and linear potential flow aerodynamics at various gust strengths, freeplay sizes, and flow velocities. Both stable and unstable responses are detected. It is found that LCO coexists with gust response for weak gust/large freeplay combinations, and it is quenched for sufficiently strong gust/small freeplay. Time marching results are provided to validate the RIDF method and confirm the findings. The present work appears to be the first use of RIDF in aeroelasticity although it is well known to nonlinear control systems analysts. Notably the RIDF method in its present form is also applicable when steady flow aerodynamic nonlinearities are included.

Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation

In this paper, 2D viscoelastic wave equation is solved numerically both on regular and irregular domains. For spatial approximation of viscoelastic wave equation two meshless methods based on local radial basis function and barycentric rational interpolation are proposed. Both of the spatial approximation methods do not need mesh, node connectivity or integration process on local subdomains so they are truly meshless. For local radial basis function method we used an existing algorithm in literature to choose an acceptable shape parameter. Time marching is performed with fourth order Runge Kutta method. L2 and L∞ error norms for some test problems are reckoned to indicate efficiency and performance of the proposed two methods. Also, stability of the methods is discussed. Acquired results confirm the applicability of the proposed methods for 2D viscoelastic wave equation. We have performed some comparisons between the proposed two methods in the sense of accuracy and computational cost. From the comparisons, we have observed that performance of the barycentric rational interpolation in the sense of accuracy is slightly better than the performance of local radial basis function however computational cost of the local radial basis function is less than the computational cost of barycentric rational interpolation.