Hasil untuk "Thermodynamics"

Philipp Pfeffer, Peter Brearley, Sylvain Laizet et al.

Abstract The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the advection–diffusion equation in a quantum computational fluid dynamics framework. The exact gate decompositions of the advection and diffusion operators in spectral space are derived. For all but the simplest one-dimensional flows, these operators do not commute. Therefore, we use operator splitting to construct quantum circuits capable of simulating arbitrary polynomial velocity profiles in multiple dimensions, such as the Blasius profile of a laminar boundary layer. Periodic, Neumann, and Dirichlet boundary conditions can be imposed with the appropriate quantum spectral transform. We evaluate the approach in statevector simulations of a Couette flow, plane Poiseuille flow, and a polynomial Blasius profile approximation. For an advection–diffusion problem in one dimension, we compare the time evolution of an ideal quantum simulation with those of real quantum computers with superconducting and trapped-ion qubits. The required number of two-qubit gates grows with the logarithm of the number of grid points raised to one higher power than the order of the polynomial velocity profile.

Xionggai Bao, Weiyuan Ma, Xin Li

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results.

Marcus Wiens, Gernot Steindl, Carlotta Tubeuf et al.

This study introduces DigiWind, an extensible digital twin platform specifically designed for the wind energy domain. The research aims to identify the fundamental requirements and architectural design for such a platform. Functional requirements are identified through a requirements engineering process using the use-case methodology. Existing digital twin and co-simulation platforms are reviewed, and the proposed DigiWind architecture is presented in detail. Three use cases are presented to highlight the integration of workflows and simulation models in the digital twin process. The DigiWind platform features a layered architecture with core implementations such as the template service, model assembly service, co-simulation service, and measurement data service. These components enable the automation of simulations, incorporation of historic measurement data, and data feedback and exchange. The platform supports various use cases including retrospective evaluation, performance monitoring, and scenario simulations. Additionally, a knowledge base and a versioning system ensure automation, documentation, and reproducibility of simulation results. The platform’s openness promotes collaboration among wind energy stakeholders and supports standardized models for co-simulation using the Functional Mock-up Interface. Overall, DigiWind offers a solution for developing, managing, and integrating digital twins in the wind energy sector, enhancing wind farm performance and operational efficiency.

Dick Bedeaux

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux–force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

G. A. Gerolymos, I. Vallet

The thermodynamic turbulence structure of compressible aerodynamic flows is often characterised by the correlation coefficient of entropy with pressure or temperature. We study entropy fluctuations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mo>′</mo></msup></semantics></math></inline-formula> and their correlations with the fluctuations of the other thermodynamic variables in compressible turbulent plane channel flow using <span style="font-variant: small-caps;">dns</span> data. We investigate the influence of the <span style="font-variant: small-caps;">hcb</span> (Huang–Coleman–Bradshaw) friction Reynolds number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>100</mn><mspace width="3.33333pt"></mspace><mspace width="-0.166667em"></mspace><mo>⪅</mo><mspace width="-0.166667em"></mspace><mspace width="3.33333pt"></mspace><mi>R</mi><msub><mi>e</mi><msup><mi>τ</mi><mo>★</mo></msup></msub><mspace width="3.33333pt"></mspace><mspace width="-0.166667em"></mspace><mo>⪅</mo><mspace width="-0.166667em"></mspace><mn>1000</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>) and of the centreline Mach number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.3</mn><mspace width="3.33333pt"></mspace><mspace width="-0.166667em"></mspace><mo>⪅</mo><mspace width="-0.166667em"></mspace><mspace width="3.33333pt"></mspace><msub><mover accent="true"><mi>M</mi><mo stretchy="false">¯</mo></mover><msub><mrow><mi>CL</mi></mrow><mi>x</mi></msub></msub><mspace width="3.33333pt"></mspace><mspace width="-0.166667em"></mspace><mo>⪅</mo><mspace width="-0.166667em"></mspace><mspace width="3.33333pt"></mspace><mn>2.5</mn></mrow></semantics></math></inline-formula>) on the magnitude and location of the peak of the root-mean-square <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>s</mi><mi>rms</mi><mo>′</mo></msubsup></semantics></math></inline-formula>. The complete series expansions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mo>′</mo></msup></semantics></math></inline-formula> with respect to the fluctuations of the basic thermodynamic variables (pressure <i>p</i>, density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> and temperature <i>T</i>) are calculated for the general case of variable heat-capacity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi>p</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> thermodynamics. The correlation coefficients of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mo>′</mo></msup></semantics></math></inline-formula> with the fluctuations of the basic thermodynamic quantities (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mrow><msup><mi>s</mi><mo>′</mo></msup><msup><mi>p</mi><mo>′</mo></msup></mrow></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mrow><msup><mi>s</mi><mo>′</mo></msup><msup><mi>ρ</mi><mo>′</mo></msup></mrow></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mrow><msup><mi>s</mi><mo>′</mo></msup><msup><mi>T</mi><mo>′</mo></msup></mrow></msub></semantics></math></inline-formula>), for varying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><msub><mi>e</mi><msup><mi>τ</mi><mo>★</mo></msup></msub><mo>,</mo><msub><mover accent="true"><mi>M</mi><mo stretchy="false">¯</mo></mover><msub><mrow><mi>CL</mi></mrow><mi>x</mi></msub></msub><mo>)</mo></mrow></semantics></math></inline-formula>, are studied. Insight on these correlations is provided by considering the probability density function (pdf) of s′ and its joint pdfs with the other thermodynamic variables.

Xiumin Yang, Fujun Zhao

In order to study the Zn(II) adsorption characteristics of hydrochloric-acid-modified bentonite in wastewater, physical characterization of hydrochloric-acid-modified bentonite was carried out, the effects of the initial concentration, reaction time, and temperature on the Zn(II) adsorption were investigated, and the adsorption kinetics and thermodynamic mechanism of the hydrochloric-acid- modified bentonite adsorption of Zn(II) were examined. The results showed that hydrochloric acid modification increased the interlayer spacing of the bentonite, and the structure of the binding between slices became looser. Hydrochloric acid modification altered the hydroxyl groups on the bentonite surface, and the hydrophilicity was enhanced. The Zn(II) adsorption capacities of bentonite and hydrochloric-acid-modified bentonite increased with the increase in the initial Zn(II) concentration, and the adsorption followed the Langmuir and Freundlich equations. The thermodynamic parameters suggested that the adsorption of Zn(II) was an endothermic, spontaneous, and entropy-increasing process. The adsorption basically reached equilibrium within 120 min, and the adsorption followed the quasi-second-order adsorption kinetic equation. The adsorption process was mainly chemical adsorption, and the intra-particle diffusion process was not the only step controlling the adsorption rate. This study provides a theoretical basis for the remediation of toxic metal wastewater and contaminated soil.

Kadhavoor R. Karthikeyan, Gangadharan Murugusundaramoorthy

Motivated by the notion of multiplicative calculus, more precisely multiplicative derivatives, we used the concept of subordination to create a new class of starlike functions. Because we attempted to operate within the existing framework of the design of analytic functions, a number of restrictions, which are in fact strong constraints, have been placed. We redefined our new class of functions using the three-parameter Mittag–Leffler function (Srivastava–Tomovski generalization of the Mittag–Leffler function), in order to increase the study’s adaptability. Coefficient estimates and their Fekete-Szegő inequalities are our main results. We have included a couple of examples to show the closure and inclusion properties of our defined class. Further, interesting bounds of logarithmic coefficients and their corresponding Fekete–Szegő functionals have also been obtained.

Candi Zheng, Yang Wang, Shiyi Chen

Extended thermodynamics commonly uses polynomial moments to model non-equilibrium transportation, but faces a crisis due to sub-shocks, which are anomalous discontinuities in gas properties when predicting shock waves. The cause of sub-shocks is still unclear, challenging the validity of extended thermodynamics. This paper reveals, for the first time, that sub-shocks arise from intrinsic limitations of polynomials leading to a discontinuous phase transition. Therefore extended thermodynamics necessitates alternative moments beyond polynomials to avoid sub-shocks.

V. V. Ryazanov

The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular, dynamic activity, are considered. A correspondence between expressions of the theory of random processes and thermodynamics of trajectories, as well as deviations from such a correspondence for the process of fluctuations of trajectory observables, are established. The connections between general regularities of first-passage times in the theory of random processes and thermodynamics of trajectories are discussed. A more complete use of the theory of random processes in physical problems is proposed, and the possibilities of combining approaches of the theory of random processes and statistical physics are indicated.

Demetrios Kotopoulis, Charis Anastopoulos

We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein's equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of the system: the Maximum Energy Principle applies when we include an entropy term from the singularity of the negative-mass solutions, in addition to the Bekenstein-Hawking term for the entropy of solutions with positive interior mass. Then, the thermodynamic analysis leads to four distinct thermodynamic phases. We also show that all types of solutions can be either thermodynamically stable or dynamically stable, but only solutions with zero interior mass can be both. Since most of our results are analytic, thin shell models emerge as a useful theoretical paradigm for exploring gravitational thermodynamics. Our results provide an additional argument in support of the assignment of entropy to the singularity of negative-mass Schwarzschild spacetimes, and, consequently, to Penrose's conjecture about the assignment of entropy to singularities.

Daniel Markthaler, Kai Peter Birke

Although originally developed to describe the magnetic behavior of matter, the Ising model represents one of the most widely used physical models, with applications in almost all scientific areas. Even after 100 years, the model still poses challenges and is the subject of active research. In this work, we address the question of whether it is possible to describe the free energy <i>A</i> of a finite-size 2D-Ising model of arbitrary size, based on a couple of analytically solvable 1D-Ising chains. The presented novel approach is based on rigorous statistical-thermodynamic principles and involves modeling the free energy contribution of an added inter-chain bond <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>A</mi><mi>bond</mi></msub><mrow><mo>(</mo><mi>β</mi><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> as function of inverse temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> and lattice size <i>N</i>. The identified simple analytic expression for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>A</mi><mi>bond</mi></msub></mrow></semantics></math></inline-formula> is fitted to exact results of a series of finite-size quadratic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>×</mo><mi>N</mi></mrow></semantics></math></inline-formula>-systems and enables straightforward and instantaneous calculation of thermodynamic quantities of interest, such as free energy and heat capacity for systems of an arbitrary size. This approach is not only interesting from a fundamental perspective with respect to the possible transfer to a 3D-Ising model, but also from an application-driven viewpoint in the context of (Li-ion) batteries where it could be applied to describe intercalation mechanisms.

Ihsan Ullah, Saeed Ahmad, Muhammad Arfan et al.

In this article, a new deterministic disease system is constructed to study the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB). The suggested model is composed of six various classes, whose dynamics are discussed in the sense of the Caputo fractional operator. Firstly the model existence of a solution along with a unique solution is checked to determine whether the system has a solution or not. The stability of a solution is also important, so we use the Ulam–Hyers concept of stability. The approximate solution analysis is checked by the technique of Laplace transformation using the Adomian decomposition concept. Such a solution is in series form which is decomposed into smaller terms and the next term is obtained from the previous one. The numerical simulation is established for the obtained schemes using different fractional orders along with a comparison of classical derivatives. Such an analysis will be helpful for testing more dynamics instead of only one type of integer order discussion.

В.А. Кульбачинский, В.Г. Кутин, И.Е. Корсаков et al.

Magnesium-doped polycrystalline ceramic samples of cooper chromite (I) have been prepared by solid phase synthesis. Phase composition and crystal structure of synthesis have been investigated by X-ray diffraction. Microstructure of samples has been investigated by scanning electron microscopy. Thermal conductivity and electrical conductivity have been measured in the temperature range 78<T<320 K. Significant reduction of thermal conductivity with an increase of synthesis duration have been observed. This effect was explained by formation of small amount of MgCr2O4 and Cr2O3 and CuO crystallites operating as effective phonon scatters. Formation of the MgCr2O4 phase is observed in X-ray diffraction patterns and SEM images of the samples with Mg content higher than 3 at. %. Formation of a small amount of Cr2O3 or CuO phase could be due to deviation of precursor’s content from stoichiometry. Obtained results open a perspective of thermoelectric figure of merit enhancement for copper chromite-based material.

Ahmed Salem, Aeshah Al-Dosari

The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>∈</mo><msubsup><mo>∫</mo><mn>0</mn><mi>σ</mi></msubsup><mo>Δ</mo><mfenced separators="" open="(" close=")"><mi>s</mi><mo>,</mo><mi>η</mi><mo>(</mo><mi>s</mi><mo>)</mo></mfenced><mi>d</mi><mi>s</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> is a multi-valued map. Relative compactness of the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mo>∫</mo><mn>0</mn><mi>σ</mi></msubsup><mo>Δ</mo><mfenced separators="" open="(" close=")"><mi>s</mi><mo>,</mo><mi>η</mi><mo>(</mo><mi>s</mi><mo>)</mo></mfenced><mi>d</mi><mi>s</mi></mrow></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mn>2</mn></msup><mfenced separators="" open="(" close=")"><mo>(</mo><mn>0</mn><mo>,</mo><mi>ε</mi><mo>)</mo><mo>,</mo><mi mathvariant="double-struck">R</mi></mfenced></mrow></semantics></math></inline-formula> is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.

Erwin T. Hegedus, Isabela R. Birs, Mihaela Ghita et al.

Fractional calculus has been opening new doors in terms of better modeling and control of several phenomena and processes. Biomedical engineering has seen a lot of combined attention from clinicians, control engineers and researchers in their attempt to offer individualized treatment. A large number of medical procedures require anesthesia, which in turn requires a closely monitored and controlled level of hypnosis, analgesia and neuromuscular blockade, as well maintenance of hemodynamic variables in a safe range. Computer-controlled anesthesia has been given a tremendous amount of attention lately. Hemodynamic stabilization via computer-based control is also a hot topic. However, very few studies on automatic control of combined anesthesia–hemodynamic systems exist despite the fact that hemodynamics is strongly influenced by hypnotic drugs, while the depth of hypnosis is affected by drugs used in hemodynamic control. The very first multivariable fractional-order controller is developed in this paper for the combined anesthesia–hemodynamic system. Simulation studies on 24 patients show the effectiveness of the proposed approach.

Iqbal Jamaludin, Mohd Zulfaezal Che Azemin, Mohd Izzuddin Mohd Tamrin et al.

The robust process in memorising the Quran is expected to cause neuroplasticity changes in the brain. To date, the analysis of neuroplasticity is limited in binary images because greyscale analysis requires the usage of more robust processing techniques. This research work aims to explore and characterise the complexity of textual memorisation brain structures using fractal analysis between huffaz and non-huffaz applying global box-counting, global Fourier fractal dimension (FFD), and volume of interest (VOI)-based analysis. The study recruited 47 participants from IIUM Kuantan Campus. The huffaz group had their 18 months of systematic memorisation training. The brain images were acquired by using MRI. Global box-counting and FFD analysis were conducted on the brain. Magnetic resonance imaging (MRI) found no significant statistical difference between brains of huffaz and non-huffaz. VOI-based analysis found nine significant areas: two for box-counting analysis (angular gyrus and medial temporal gyrus), six for FFD analysis (BA20, BA30, anterior cingulate, fusiform gyrus, inferior temporal gyrus, and frontal lobe), and only a single area (BA33) showed significant volume differences between huffaz and non-huffaz. The results have highlighted the sensitivity of VOI-based analysis because of its local nature, as compared to the global analysis by box-counting and FFD.

Robert Hołyst, Karol Makuch, Anna Maciołek et al.

There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that $U$ satisfies the following equation $dU=T^{*}dS^{*}-pdV$ for a constant number of particles, irrespective of the shape of the container, boundary conditions, size of the system, or mode of heat transfer into the system. We calculate $S^{*}$ and $T^{*}$ explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.

Takashi Arima, Maria Cristina Carrisi, Sebastiano Pennisi et al.

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

Victoria V. Golovina, Pavel P. Rymkevich, Ekaterina A. Shakhova et al.

The paper presents a study of the deformation properties of polymer materials. The authors consider the effect of the temperature factor, unaccounted for previously in modeling and forecasting, on the deformation properties of polymer filaments and the influence of changes in material temperature during deformation. The derivations of the main thermodynamic functions for polymer materials are given. The work examines the energy diagram typical for polymers that shrink. An explanation is given for the “dormancy” of the recovery process, as well as for the identical values of the highly elastic deformation when the load is removed during the recovery process in polymer threads and films. Based on the equation of condition for polymer filament and the well-known thermodynamic identities, the following basic thermodynamic functions were determined: internal energy, enthalpy and entropy depending on temperature and dimensionless stress. The cases of application of the first law of thermodynamics to deformation processes are examined. From the standpoint of thermodynamics, the main models of deformation are considered, i.e. creep, stress relaxation and active stretching of polymer filaments and films. Explanations are given for some of the phenomena observed experimentally in course of these processes. It was concluded that it is necessary to take into account the change in local temperature. Based on the model on the equation of condition for polymer filament and the analogue of the Clapeyron- Clausius equation, an expression for the temperature coefficient of material pressure is obtained. The work enabled to explain the “dormancy” of the recovery process of polymer and to determine the basic thermodynamic functions for a polymer material which take into account the material temperature change during deformation. The thermodynamic coefficient for the polytropic process is obtained. The described temperature coefficient makes it possible to analyze the tensile diagrams depending on the strain rate and the temperature change rate of the sample. The highly elastic part of deformation in thermodynamic function is expressed through the elastic deformation determined by the mechanical stress, which can be measured directly during the experiment.

Mehdi Mostafaiyan, Sven Wießner, Gert Heinrich et al.

We introduce an improved conservative direct re-initialization (ICDR) method (for two-phase flow problems) as a new and efficient geometrical re-distancing scheme. The ICDR technique takes advantage of two mass-conserving and fast re-distancing schemes, as well as a global mass correction concept to reduce the extent of the mass loss/gain in two- and three-dimensional (2D and 3D) problems. We examine the ICDR method, at the first step, with two 2D benchmarks: the notched cylinder and the swirling flow vortex problems. To do so, we (for the first time) extensively analyze the dependency of the regenerated interface quality on both time-step and element sizes. Then, we quantitatively assess the results by employing a defined norm value, which evaluates the deviation from the exact solution. We also present a visual assessment by graphical demonstration of original and regenerated interfaces. In the next step, we investigate the performance of the ICDR in three-dimensional (3D) problems. For this purpose, we simulate drop deformation in a simple shear flow field. We describe our reason for this choice and show that, by employing the ICDR scheme, the results of our analysis comply with the existing numerical and experimental data in the literature.