Artificial Oscillations Research Articles

Finite size effects and optimization of the calculation of the surface tension in surfactant mixtures at liquid/vapour interfaces

The surface tension of monolayers with mixtures of anionic and nonionic surfactant at the liquid/vapour interface is studied. Previous works have observed that calculations of the surface tension of simple fluids show artificial oscillations for small interfacial areas, indicating that the surface tension data fluctuate due to the finite size effects and periodic boundary conditions. In the case of simulations of monolayers composed of surfactant mixtures, the surface tension not only oscillates for small areas but can also give non-physical data, such as negative values. Analysis of the monolayers with different surfactant mixtures, ionic (DTAB, CTAB, SDS) and nonionic (SB3-12), was done for density profiles, parameters of order and pair correlation functions for small and large box areas and all of them present similar behaviour. The fluctuations and the non-physical values of the surface tension are corrected when boxes with large interfacial areas are considered. The results indicate that in order to obtain reliable values of the surface tension, in computer simulations, it is important to choose not only the correct force field but also the appropriate size of the simulation box.

Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids

AbstractSymplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occurring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behavior. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution.

Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution using higher-order continuous B-spline basis functions in both spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method.

An improved high-accuracy interpolation method for switching devices in EMT simulation programs

This paper presents an interpolation with Backward Euler (BE) method that enhances the switching simulations accuracy in an electromagnetic transient (EMT) simulation with a fixed time-step. Because of the switching operations on discrete instants, the simulations can show artificial voltage spikes and numerical oscillations (chatter), compromising the accuracy and producing misleading results. We thus present a method that eliminates the spurious switching losses and improves the accuracy by combining interpolation and extrapolation with a half-time-step BE solution over existing interpolation-based approaches to resolve the issues above. In addition, this improved method requires the same calculation steps as the industry-accepted instantaneous interpolation. Analytical discussion reinforced by the simulation studies for a simple and complex power electronic circuits demonstrates the accuracy and efficacy of the proposed interpolation with BE method.

Simplification of contour lines, based on axial splines, with high-quality results

This paper introduces a new simplification method providing high-quality contour lines derived from the 3D point cloud, minimizing their energy. It combines the simplification potential and the splines with the generalized axial symmetry. Generating results similar to the topological skeleton, it applies to large-scale maps (1:5000–1:25,000). It significantly improves all geometric and shape parameters of contour lines, namely in flatter areas. Extensive cartographic testing on high spatial density point clouds using 17 invariants is performed. The outcomes indicate the significant potential of the proposed method. The simplified contour lines preserve the given vertical error, lie within the vertical buffer, are parallel, aesthetically pleasing, and have similar spacing; their artificial oscillations are significantly reduced. Unlike complex generalization methods, the proposed solution does not interfere with the DTM but performs only a correction of the cartographic representation of contour lines.

Transition moments beyond the electric-dipole approximation: Visualization and basis set requirements.

In the simulation of x-ray absorption spectroscopy, the validity of the electric-dipole approximation comes into question. Three different schemes exist to go beyond this approximation: the first scheme is based on the full semi-classical light-matter interaction, whereas the latter two schemes, referred to as the generalized length and velocity representation, are based on truncated multipole expansions. Even though these schemes have been successfully implemented in several quantum chemistry codes, their basis set requirements remained largely unknown. Here, we assess basis set requirements of these three schemes. We have considered 1s1/2 and 7s1/2 → 7p1/2 transitions in the radium atom, representative of core and valence excitations, respectively, and carried out calculations with dyall.aeXz (X = 2, 3, 4) basis sets at the four-component relativistic TD-HF level of theory. Our basis set study was greatly facilitated by the generation and visualization of radial distributions of transition moment densities, allowing for a straightforward comparison with equivalent finite-difference calculations. Pertaining to the truncated interaction, we find that the length representation electric multipole is the easiest to converge, requiring the dyall.ae2z basis for low-order multipoles and the dyall.ae4z basis at higher orders. The magnetic multipole moments follow a similar trend although they are more difficult to converge. The velocity representation electric multipoles are the most difficult to converge: at high orders, the dyall.ae3z and dyall.ae4z basis sets introduce artificial peaks and oscillations, which increase the overall error. These artifacts are associated with linear dependence issues in the small component space of larger basis sets. The full interaction operator, however, does not suffer from these problems, and we therefore recommend its use in the simulation of x-ray spectroscopy.

Customizable adaptive regularization techniques for B-spline modeling

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. The proposed method selectively incorporates regularization terms based on first and second derivatives to maintain model accuracy while minimizing numerical artifacts. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations. In addition, a key tuning parameter is highlighted and the effects of this parameter are presented in detail. This paper is an extension of our previous conference paper at the 2022 International Conference on Computational Science (ICCS) (Lenz et al., 2022) [1].

A Penalty Method for Coupling of Finite‐Element and Peridynamic Models

AbstractA classical continuum mechanics model no longer fulfills its basic assumptions, when the deformations are not smooth or discontinuous. Peridynamics (PD) as an integral formulation could better overcome these issues. Therefore, it is better suited to solve fracture problems such as crack initiation, its growth and formation of crack patterns. In PD the magnitudes of internal forces at a material point depend on the collective interaction of all material points within a subdomain called horizon. To take advances from the formulation, typically it is implemented in a mesh‐free form. In that case, it is easy to separate interactions between different material points. As consequence, a relatively high resolution is required to describe continuous deformation functions and, consequently computationally expensive. Therefore, the application of mesh‐free PD in undamaged regions requires an unnecessary high effort for receiving sufficient accurate results. In contrast, the finite element method (FEM) as a classical continuum mechanics‐based approach, is very efficient, if continuous stress distributions can be assumed. Consequently, a computational cost reduction can be achieved, if the PD is applied in the local damaged zone only and the remaining area is modeled and analyzed with the classical FEM. Realization of such an approach requires a sufficient accurate coupling of the PD and the FEM subdomains.A brief overview about different coupling approaches is given. Then the general approach of an Arlequin based method is presented. Here the coupling is achieved via an overlapping of PD and FEM areas. The coupling equations are developed and realized with help of the Penalty method. The Penalty method is considered as an alternative procedure to the Lagrange multiplier strategy without creating new unknowns, which essentially simplifies the coupled PD‐FEM approach. The validity and limits of the proposed technique are demonstrated through analysis, where the choice of the Penalty number is discussed as well as artificial wave oscillations, caused by the coupling area.

Сравнение способов аппроксимации функции множителей Лагранжа при решении контактных задач методом с независимой границей контакта

The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

Oscillation-free source term inversion of atmospheric radionuclide releases with joint model bias corrections and non-smooth competing priors

The source term of atmospheric radionuclide releases is essential for the hazardous consequence assessment and emergency response. However, the artificial release oscillations in the source term estimate remain a fundamental challenge and may deliver misleading information, because of the unavoidable model biases and observation uncertainties. We propose a new method that removes oscillations while recovering the release details. This method explicitly corrects the model biases using the joint correction model and compensates the observation uncertainties through non-smooth competing priors that involve two rival functions. The new priors better model the unsteady feature of the radionuclide releases and distinguish the true releases from oscillations, enabling release-preserving oscillation removal. We extend the projected alternating minimization algorithm for an efficient solution. The method achieves oscillation-free and nearly perfect profiles for real releases of the Perfluoro-Methyl-Cyclo-Hexane on continental and regional scales, and the radionuclide 41Ar on a local scale, outperforming state-of-the-art and very recent methods. The sensitivities to model inputs and key parameters are also investigated. Robust performance is exhibited under emissions of both radioactive and non-radioactive substances, different meteorological inputs and numbers of observations, paving the way for identifying dynamic atmospheric radionuclide releases at multiple scales, especially when the release status is unknown.

A fifth-order low-dissipation discontinuity-resolving TENO scheme for compressible flow simulation

For compressible flows characterized by a wide range of flow length scales and discontinuities, it is still an open challenge to design the optimal schemes, which resolve the small-scale flow structures with low numerical dissipation and capture the shock waves without artificial oscillations. In Takagi et al. [1], a novel TENO5-THINC scheme with the combination of classical TENO5 (fifth-order Targeted Essentially Non-Oscillatory) scheme and the non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) reconstruction has been proposed. Building upon the strategy of isolating discontinuities from smooth and high-wavenumber regions, in the present work, a new very low-dissipation TENO scheme with discontinuity-resolving property is proposed for compressible flow simulations based on three new concepts: (1) an improved discontinuity-detecting criterion is devised based on the TENO weighting strategy, which significantly enhances the discontinuity-detecting accuracy compared to that in TENO5-THINC; (2) A local interpolation-like strategy is proposed to represent the detected discontinuity with subcell resolutions, and this strategy can minimize the numerical dissipation even when compared to the THINC reconstruction scheme; (3) According to the varying sharpness of the discontinuities separated by the discontinuity-detecting indicator, the local interpolation-like strategy is extended with a two-steepness approximation. Specifically, the discontinuities will be classified as genuinely sharp discontinuities and general ones. For the genuinely sharp discontinuities, the interface flux will be estimated by a steeper step-like function with even less numerical dissipation. The resulting scheme maintains the high-order and low-dissipation properties of the TENO scheme for smooth flow scales, while further improving the discontinuity-resolving capability and suppressing the numerical oscillations in the vicinity of discontinuities. A variety of benchmark cases with broadband length scales as well as discontinuities is presented to demonstrate the high wave-resolution property and the sharp shock-capturing capability of the proposed scheme.

Mitigating the numerical xenon instability in deterministic reactor burnup calculations

Depletion methods used in modern core simulators for thermal-spectrum reactor burnup calculations may be predisposed to activating, under the correct conditions, a numerical instability that presents itself in the form of artificial spatial xenon oscillations. In this paper a three-dimensional pressurised water reactor depletion problem is utilised to demonstrate that one of the most widely used predictor-corrected depletion schemes can be afflicted by numerical xenon instabilities in reactor burnup calculations performed with a state-of-the-art nodal diffusion core simulator. A method which results in tightening the algorithmic coupling between the 135Xe transmutation and the neutron flux computation steps is proposed for mitigating the numerical xenon instability. The method is called the Xenon Transmutation Feedback (XeTF) method because it incorporates 135Xe transmutation in the feedback iterations of a neutronics solver. The effectiveness of the method is verified by numerical evaluation of some typical reactor depletion scenarios.

Progress in two-phase flow modeling: Interfacial area transport

The interfacial area transport equation (IATE) employs a dynamic approach to predict interfacial area concentration (IAC) in two-phase flows. It eliminates the need for the static flow regime transition criteria and flow regime dependent IAC correlations used in closing the two-fluid model and therefore any potential artificial bifurcation or numerical oscillations stemming from these static correlations. The efforts to develop the IATE are reviewed in this work, focusing on studies within the past decade. The current state-of-the-art in IATE is a two-group interfacial area transport equation that is applicable to predict interfacial area concentration from bubbly to churn-turbulent flows. An extensive experimental database has been established in literature for various two-phase flow conditions. The database is used to develop constitutive models to close the IATE and to validate its performance. These include adiabatic and heated conditions, vertical and horizontal flow orientations, channels with flow restrictions, round, rectangular, annulus, and rod-bundle geometries, and normal-gravity and reduced-gravity conditions. IATE has been implemented into practical system analysis codes such as TRACE and computational fluid dynamics (CFD) codes such as CFX and Fluent to evaluate its performance. In addition, the recent efforts of extending the IATE beyond churn-turbulent flow to churn-annular transition and annular flows are also reviewed. These include the new instrumentation, experimental database, and additional constitutive models to predict annular flows.

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation (4D-Var) has been widely used in meteorological and oceanographic data assimilation. This method is usually implemented in the model space, known as primal approach (P4D-Var). Alternatively, physical space analysis system (4D-PSAS) is proposed to reduce the computation cost, in which the 4D-Var problem is solved in physical space (i.e., observation space). In this study, the conjugate gradient (CG) algorithm, implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process. The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed. In order to overcome the non-monotonic variation of gradient norm, a new algorithm, Minimum Residual (MINRES) algorithm, is implemented in the process of assimilation iteration in this study. Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function, greatly improves the convergence properties of 4D-PSAS as well, and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

Influence of coupling approximation on the numerical stability of explicit co-simulation

Co-simulation allows the parallelization of several subsystems in a distributed manner with data exchanges at discrete user-defined communication points (macro-time points). Between two macro-time points, subsystems are integrated in a local circumstance using specified solvers. By adopting the technique, the computational efficiency can be enhanced greatly without exposure of inner information. As a weak coupling, communication between subsystems is usually approximated by extrapolated or interpolated polynomials that may induce instability. Implicit or semi-implicit co-simulation with iteration of macro-time steps can improve stability behavior significantly. However, reinitialization may be unfeasible for realtime simulation or not supported by most commercial tools. Therefore, stabilized non-iterative co-simulation has been more popular that can be achieved either by appropriate communication techniques or by interface error estimations. However, the influence of the coupling approximations on numerical stability is not well understood. In this paper, the numerical stability of explicit co-simulation will be studied using different approximations of coupling techniques. The influence of communication schemes (parallel and sequential coupling scheme), least square as well as relaxation techniques using an applied force coupling approach will be investigated quantitatively with the help of a linear two-mass oscillator. A quarter car model is used to validate the stability analysis of the linear oscillator. The results indicate that by adopting appropriate coupling techniques, stability improvement can be accomplished. Higher order of extrapolation (interpolation) introduces damping to the distributed system while relaxation and least square approaches might trigger artificial oscillations.

Numerical analysis and optimization of triggered furrow irrigation system

Numerical methods have been proved to be useful tools for understanding different phenomena. In this paper, triggered furrow irrigation has been analyzed by means of numerical modeling. To this end, a special code is developed for simulation of triggered furrow irrigation system by coupling three-dimensional Richards’ equation and one-dimensional fully hydrodynamic form of Saint-Venant equations. The coordinate transformation technique was used for solving Richards’ equation that improves flexibility of model for simulation of water flow in irregularly shaped furrows. Furthermore, overland flow module benefits from high-resolution total variation diminishing scheme that avoids artificial oscillations commonly occurring on the advance water front. The code was validated against different analytical, numerical and experimental benchmarks. In all cases, the accuracy of model was acceptable. The code was subsequently employed to simulate all phases of triggered furrow irrigation system (including advance and redistribution phases) on a field cultivated with wheat. Finally, Taguchi technique was employed to deduct proposals to optimize performance of triggered furrow irrigation system in terms of sensor position, triggering and cutoff thresholds and inflow rate. It was concluded that optimal performance of triggered irrigation system was obtained when the water content sensor was installed close to the furrow, providing that triggering and cutoff thresholds were set as − 15 and − 3 m (close to field capacity) and inflow rate was 1 L s−1.

Numerical artifacts associated with Rayleigh and modal damping models of inelastic structures with massless coordinates

SummaryThe paper presents a detailed reexamination of the effects of three damping models on the inelastic seismic response of structures with massless degrees of freedom. The models considered correspond to (a) Rayleigh damping based on current properties (tangent stiffness), (b) Rayleigh damping based on initial properties, and (c) modal damping. The results suggest that some nonzero damping forces/moments at massless DOFs obtained in multistory frames for the case of Rayleigh damping with tangent stiffness may be numerical artifacts rather than a deficiency of the damping model. The results also indicate that significant artificial numerical oscillations in the velocities of the secondary components of MDOF structures are introduced when modal damping or mass‐proportional damping is used.

Direct contact heat transfer enhancement between two stratified immiscible fluids by artificial interface oscillations

Direct contact heat transfer between stratified immiscible fluids is commonly encountered in solar salt industry, desalination, petrochemical engineering, etc. Usually, the mutual mixing and penetration between stratified flows are weak, and hence the heat and mass transfer rates are quite limited and act as an obstacle in their wider applications. Considering the fact there is always clear surface (interface) between immiscible fluids, this study proposes to stimulate interface oscillations artificially to reinforce the mixing between fluids and thus enhance the transfer processes. The artificial oscillations employed in this paper are sinusoidal wave and their amplitude, period and wave length on the direct contact heat transfer between stratified airstream and water surface are investigated respectively. Heat transfer was found to be enhanced to a great extent by artificial oscillations, ranging from one to three times higher than that without oscillations. With the amplitude, period and wave length covered in this study ranging from 1 mm to 4 mm, 0.1 s to 2 s, and 40 mm to 100 mm, respectively, the heat transfer enhancement effect was found to increase with increase of oscillation amplitude and decrease of wave length, and this effect became more distinct at higher airstream velocity. However, the change of oscillation periods covered in this study shows minor difference on the heat transfer enhancement. Without using special solid inserts or alternation to the heat exchanger structure, artificial oscillation of phasic interface can be a simple and efficient technique to enhance transfer process between stratified flows.

Use of fiber-optic distributed temperature sensing to investigate erosion of the non-convective zone in salt-gradient solar ponds

Salt-gradient solar ponds (SGSPs) collect and store solar radiation as thermal energy. This thermal energy is stored in the pond’s bottom because of the existence of the non-convective zone (NCZ), a layer comprised by a salinity gradient that results in a stable density profile, which suppresses global convection within the pond. As a consequence, the NCZ is the most important layer of an SGSP that must be maintained to sustain the internal structure of the pond and to allow successful thermal energy storage. The NCZ is characterized by a thermal gradient and thus, the internal structure of an SGSP can be inferred using temperature measurements. In this work, fiber-optic distributed temperature sensing (DTS) methods are systematically assessed in a laboratory-scale SGSP, and a simple interface tracking algorithm to determine the NCZ evolution – based on thermal measurements – is presented. To evaluate this algorithm, a DTS system and a discrete array of 14 point-in-space temperature loggers were used to record temperatures in the laboratory-scale SGSP. Acceptable results regarding the NCZ evolution were achieved with the discrete array of sensors. However, much better results were obtained with the DTS high-spatial resolution measurements, despite the presence of some artificial thermal oscillations in the DTS records. These oscillations did not affect the results of the interface tracking algorithm, but may be a concern on large-scale field installations. It was also found that the location of the NCZ boundaries can be determined even with low spatial resolution measurements. However, this determination can only be achieved using the proper interpolation method.

Lattice Boltzmann solution of advection-dominated mass transport problem: a comparison

This article addresses the abilities and limitations of the Lattice Boltzmann (LB) method in solving advection-dominated mass transport problems. Several schemes of the LB method, including D2Q4, D2Q5, and D2Q9, were assessed in the simulation of two-dimensional advection-dispersion equations. The concept of Single Relaxation Time (SRT) and Multiple Relaxation Time (MRT) in addition to linear and quadratic Equilibrium Distribution Functions (EDF) were taken into account. The results of LB models were compared to the well-known Finite Difference (FD) solutions, including Explicit Finite Difference (EFD) and Crank-Nicolson (CN) methods. All LB models are more accurate than the aforementioned FD schemes. The results also indicate the high potency of D2Q5 SRT and D2Q9 SRT in describing advection-controlled mass transfer problems. The numerical artificial oscillations are observed when the Grid Peclet Number (GPN) is greater than 10, 25, 20, 25, and 10 regarding D2Q4 SRT, D2Q5 SRT, D2Q5 MRT, D2Q9 SRT and D2Q9 MRT, respectively, while the corresponding GPN values obtained for the EFD and CN methods were 2 and 5, respectively. Finally, a coupled system of groundwater and solute transport equations were solved satisfactorily using several LB models. Considering computational time, all LB models are much faster than CN method.