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A splitting technique for solutions of the Navier—Stokes and the energy equations, in Boussinesq approximately, is presented. The equations are first integrated in time using a splitting procedure and then discretized spatially by means of a high‐order spectral element method. The whole technique is validated on the flow in a differentially‐heated cavity at intermediate and transitional Rayliegh numbers. The results are in a very good agreement with other available numerical solutions.

The purpose of this paper is to propose an efficient/robust numerical algorithm for solving the two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element (FE) technique.

A numerical algorithm was based on the so‐called consistent splitting scheme, which improved the numerical accuracy of the primitive variables. In order to obtain a stable solution, two choices of mixed FEs, the Taylor‐Hood and Crouzeix‐Raviart types, were used. Two mesh layouts were considered; uniform and non‐uniform.

To verify that the proposed scheme had a second‐order accuracy, some numerical results are presented and compared with the known solution. The answer was confirmative. Numerically accurate solutions were obtained for a fixed Prandtl number, Pr=0.71, for a range of the Reynolds number, Re from 100 to 3,000, and for a range of the Richardson number, Ri from 0.001 to 100. The results from these calculations, using the mixed FE consistent splitting scheme, agreed with the existing ones.

Further extensions of this work could include the influence of various choices of Reynolds numbers, Prandtl numbers and Richardson numbers, and the effect of aspect ratio.

The present work was the first to apply a mixed FE in association with the consistent splitting scheme to the mixed convection problem.

This paper aims to design and analyze implicit/explicit/semi-implicit schemes and a universal error estimator within the Generalized Single-step Single-Solve computational framework for First-order transient systems (GS4-I), which also fosters the adaptive time-stepping procedure to improve stability, accuracy and efficiency applied for fluid dynamics.

The newly proposed child-explicit and semi-implicit schemes emanate from the parent implicit GS4-I framework, providing numerous options with flexible and controllable numerical properties to the analyst. A universal error estimator is developed based on the consistent algorithmic variables and it works for all the developed methods. Applications are demonstrated by merging the developed algorithms into the iterated pressure-projection method for incompressible Navier–Stokes equations.

The child-explicit GS4-I has improved solution accuracy and stability properties, and the most stable option is the child explicit GS4-I(0,0)/second-order backward differentiation formula/Gear’s methods, which is new and novel. Numerical tests validate that the universal error estimator emanating from implicit designs works well for the newly proposed explicit/semi-implicit algorithms. The iterative pressure-correction projection algorithm is efficiently fostered by the error estimator-based adaptive time-stepping.

The implicit/explicit/semi-implicit methods within a unified computational framework are easy to implement and have flexible options in practical applications. In contrast to traditional error estimators, which work only on an algorithm-by-algorithm basis, the proposed error estimator is universal. They work for the entire class of implicit/explicit/semi-implicit linear multi-step methods that are second-order time accurate. Based on the accurately estimated local error, balance amongst stability, accuracy and efficiency can be well achieved in the dynamic simulation.

The purpose of this paper is to perform two-dimensional numerical simulation involving fluid-structure interaction of flexible filament. The filament is tethered to the bottom of a rectangular channel with oscillating fluid flow inlet conditions at low Reynolds number. The simulations are performed using a temporal second-order finite volume-based immersed boundary method (IBM). Further, to understand the relation between different aspect ratios i.e. ratio of filament length to channel height (Len/H) and fixed channel geometry ratio, i.e. ratio of channel height to channel length (H/Lc) on mixing and pumping capabilities.

The discretization of governing continuity and Navier–Stokes equation is done by finite-volume method on a staggered Cartesian grid. SIMPLE algorithm is used to solve fluid velocity and pressure terms. Two cases of oscillatory flow conditions are used with the flexible filament tethered at the center of bottom channel wall. The first case is sinusoidal oscillatory flow with phase shift (SOFPS) and second case is sinusoidal oscillatory flow without phase shift (SOF). The simulation results are validated with filament dynamics studies of previous researchers. Further, parametric analysis is carried to study the effect of filament length (aspect ratio), filament bending rigidity and Reynolds number on the complex deformation and behavior of flexible filament interacting with nearby oscillating fluid motion.

It is found that selection of right filament length and bending rigidity is crucial for fluid mixing scenarios. The phase shift in fluid motion is also found to critically effect filament displacement dynamics, especially for rigid filaments. Aspect ratio, suitable for mixing applications is dependent on channel geometry ratio. Symmetric deformation is observed for filaments subjected to SOFPS condition irrespective of bending rigidity, whereas medium and low rigidity filaments placed in SOF condition show severe asymmetric behavior. Two key findings of this study are: symmetric filament conformity without appreciable bending produces sweeping motion in fluid flow, which is highly suited for mixing application; and asymmetric behavior shown by the filament depicts antiplectic metachronism commonly found in beating cilia. As a result, it is possible to pin point the type of fluid motion governing fluid mixing and fluid pumping. The developed computational model can, thus, successfully demonstrate filament-fluid interaction for a wide variety of similar problems.

The present study uses a temporal second-order finite volume-based IBM to examine flexible filament dynamics for various applications such as fluid mixing. Also, it highlights the relationship between channel geometry ratio and filament aspect ratio and its effect on filament sweep patterns. The study further reports the effect of filament displacement dynamics with or without phase shift for inlet oscillating fluid flow condition.

To present a numerical method for the solution of the unsteady incompressible Navier‐Stokes equations in a generic setting.

The equations are discretized in space by the finite element method, and in time by a semi‐implicit finite difference scheme, using a fractional‐step method to enforce incompressibility.

The presented results demonstrate the satisfactory accuracy of the method in the simulation of vortical flows in laminar regime and the stability of the solution in presence of a strong boundary layer.

The successful integration of the CFD into the industrial design depends on its capability to produce accurate and reliable simulations of real life applications. These considerations drive the development of the proposed method: it can be used in conjunction with finite elements of any order of accuracy, providing accurate and numerically stable results for complex flows. Moreover, the computational requirements are low when compared with other similar strategies.

This chapter provides a presentation about Chapter 1 of The Balance of the National Economy, 1923–24, edited by Pavel Illich Popov. The Balance was issued in June 1926 by the Central Statistical Administration (CSU or TsSU) of the USSR, which Popov had headed from July 1918 to January 1926. In the first part of our chapter, we show how Popov’s work on the balance of the national economy was rooted in the specific scientific and political culture of zemstvo statisticians inherited from the Tsar. Statistical inquiry was considered an objective scientific process based on international standards. Furthermore, like zemstvo statisticians, CSU statisticians developed great autonomous political power. The balance of the national economy was built according to these principles, which met harsh criticism from revolutionaries and Bolsheviks. In the second part, we analyze the contents of Popov’s Chapter 1, especially the theoretical foundations of the balance and its connection with Soviet planning. In the third part, we discuss the balance’s significance in the years 1926–1929, years which ended the NEP and launched the first Five-Year Plan, so as to understand how CSU’s balance didn’t become a standard Soviet statistical instrument and was discarded as a “bourgeois” device.

This paper aims to improve the computational efficiency of higher-order accurate Noye–Hayman [NH (9,9)] implicit finite difference scheme for the solution of electromagnetic scattering problems in tunnel environments.

The proposed method consists of two major steps: First, the higher-order NH (9,9) scheme is numerically discretized using the finite-difference method. The second step is to use an algorithm based on hierarchical interpolative factorization (HIF) to accelerate the solution of this scheme.

It is observed that the simulation results obtained from the numerical tests illustrate very high accuracy of the NH (9,9) method in typical tunnel environments. HIF algorithm makes the NH (9,9) method computationally efficient for two-dimensional (2D) or three-dimensional (3D) problems. The proposed method could help in reducing the computational cost of the NH (9,9) method very close to O(n) usual O(n3) for a full matrix.

For simplicity, in this study, perfect electric conductor boundary conditions are considered. Future research may also include the utilization of meteorological techniques, including the effects of backward traveling waves, and make comparisons with the experimental data.

This study is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.

The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time.

The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems.

For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

When wearable and implantable devices first arose in the 1970s, they were rigid and clashed dramatically with our soft, pliable skin and organs. The past two decades have witnessed a major upheaval in these devices. Traditional electronics are six orders of magnitude stiffer than soft tissue. As a result, when rigid electronics are integrated with the human body, severe challenges in both mechanical and geometrical form mismatch occur. This mismatch creates an uneven contact at the interface of soft-tissue, leading to noisy and unreliable data gathering of the body’s vital signs. This paper aims to predict the role that discreet, seamless medical devices will play in personalized health care by discussing novel solutions for alleviating this interface mismatch and exploring the challenges in developing and commercializing such devices.

Since the form factors of biology cannot be changed to match those of rigid devices, conformable devices that mimic the shape and mechanical properties of soft body tissue must be designed and fabricated. These conformable devices play the role of imperceptible medical interfaces. Such interfaces can help scientists and medical practitioners to gain further insights into the body by providing an accurate and reliable instrument that can conform closely to the target areas of interest for continuous, long-term monitoring of the human body, while improving user experience.

The authors have highlighted current attempts of mechanically adaptive devices for health care, and the authors forecast key aspects for the future of these conformable biomedical devices and the ways in which these devices will revolutionize how health care is administered or obtained.

The authors conclude this paper with the perspective on the challenges of implementing this technology for practical use, including device packaging, environmental life cycle, data privacy, industry partnership and collaboration.