Semi-implicit Algorithm Research Articles

Fluid Dynamic and Thermal Performance of a V-Shape Slotted Cylinder

The flow characteristics and thermal performance of circular cylinders with V-shape slots are investigated numerically. The simulation is a two-dimensional incompressible flow that employs the semi-implicit finite volume multi-material algorithm MPM-ICE, which is a module of the Uintah framework. The normalized slot width s2/D ranges from 0.1 to 0.2, and the corresponding increases in total surface area are from ~99% to ~70%, respectively. Compared to the solid cylinder, the slotted cylinder has the largest total drag reduction of ~67% at s2/D of 0.2. Meanwhile, although the heat transfer is proportional with the surface area, the thermal performance of the V-shape slot first improves with the slot width, and then declines. The heat transfer improvement has an optimum value of ~192% at s2/D of 0.15. The overall slot performance, defined by the ratio of the heat transfer to the drag force, is best at 0.175.

Study on unified strength theory and elastic–plastic stress update algorithm

The unified strength theory with the two-piecewise linear equations is more convenient and concise to calculate the strength of materials. It can fully explore the potential in the strength of materials and improve the economic benefits of engineering design. This study combines the semi-implicit return mapping algorithm and the Aitken accelerated iteration scheme and develops a plastic constitutive algorithm for isotropic softening materials based on the unified strength theory. The combining method can simplify the stress update and make the calculation of consistent tangent modulus easier. Furthermore, it can avoid solving the partial derivatives of the plastic flow rule and overcome the stress-deviating problem. The self-developed constitutive algorithm is used to simulate the elastic–plastic excavation process of a deep-lying circular tunnel. The numerical simulation results match well with the theoretical solution, verifying the correctness of the self-developed constitutive algorithm. Based on the self-developed constitutive algorithm, the stability of an underground mining stope is comprehensively analyzed, and its structural parameters are optimized. The research reveals the mechanism of stope instability, provides a reliable scientific basis for the mining design and decision-making, ensures the safe and efficient production of the stope, and achieves the expected goal.

A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows

This paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows, interacting with moving solid obstacles. A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase, a solid phase, and the surrounding void. According to the so-called diffuse interface approach, the different phases and consequently the void are described by means of a scalar volume fraction function for each phase. In our numerical scheme, the dynamics of the liquid phase and the motion of the solid are decoupled. The solid is assumed to be a moving rigid body, whose motion is prescribed. Only after the advection of the solid volume fraction, the dynamics of the liquid phase is considered. As usual in semi-implicit schemes, we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly, while the pressure terms are treated implicitly. The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach. The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique. The time step size is only limited by the velocities of the two phases contained in the domain, and not by the gravity wave speed nor by the stiff algebraic relaxation source term, which requires an implicit discretization. The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.

Coexistence of passive vortex-induced vibrations and active pitch oscillation triggered by a square cylinder attached with a deformable splitter plate

To understand passive vortex-induced vibrations (VIV) coexisting with active structure motions, this paper numerically investigates the use of pure pitch oscillation to control a square cylinder mounted with a deformable splitter plate at the Reynolds number of 333. The oscillation is enforced with an amplitude of 3° and different frequencies from 0 to 6 Hz. Direct numerical simulations using a partitioned method with a semi-implicit coupling algorithm are performed. According to the trajectories of the splitter-plate tip displacement with respect to the lift or drag force coefficient, a specific lock-in regime determined by the frequency of the enforced pitch oscillation is identified. Further spectral analyses of the tip displacement and lift force show that the lock-in frequencies are equal to the enforced frequencies. Next to the lock-in regime, semi-lock-in regimes with narrow bandwidths are distinguished, exhibiting both lock-in and non-lock-in features. In the non-lock-in regimes, the frequencies of the most predominant peaks in the spectra are found near the natural frequency of the splitter plate of 3.236 Hz, and the frequencies of the two secondary peaks are distributed along the characteristic lines following the ratios of these frequencies to the enforced frequency, which are ±1. Thus, the interaction is dependent on the combined effects of the passive VIV and the actively enforced pitch oscillations. Moreover, the intersection points of the characteristic lines are located close to the upper and lower frequency limits of the lock-in regime, inferring the conditions for the lock-in onset.

The semi-implicit DLN algorithm for the Navier-Stokes equations

Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order, A-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{A}-$$\\end{document} and G-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{G}-$$\\end{document} stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified by the refactorization process (adding time filters on the backward Euler scheme). Due to these fine properties, the DLN method has strong potential for the numerical simulation of time-dependent fluid models. In the report, we propose a semi-implicit DLN algorithm for the Navier-Stokes equations (avoiding non-linear solver at each time step) and prove the unconditional, long-term stability, and second-order convergence with the moderate time step restriction. Moreover, the adaptive DLN algorithms by the required error or numerical dissipation criterion are presented to balance the accuracy and computational cost. Numerical tests will be given to support the main conclusions.

Phase-field crystal simulation of the evolution of voids in polycrystalline Au–Al bonds with elastic interaction and the Kirkendall effect

In this paper, the modified phase-field crystal (MPFC) model is employed to study the evolution of Kirkendall voids in polycrystalline Au–Al bonds under mechanical loading. The MPFC model can simulate the structural evolution of deformed pure nanocrystalline materials considering instantaneous elastic interactions. Therefore, coupling a concentration field evolved by the Cahn-Hilliard equation with a density field evolved by the existing MPFC model makes it possible to study the phase transformation of a binary system in the presence of mechanical deformation. Using this modified model, we focus on the morphology evolution of the voids in Au–Al bonds under different mechanical loadings. The semi-implicit Fourier spectral algorithm is applied to solve the six-order coupling dynamics equations. The Kirkendall porosity of the diffusion couple is computed and analyzed. The effects of quasi-static and cyclic axial tensile loads on the morphology of voids, and porosity of the system are investigated. It is found that the morphology of Kirkendall voids that result from applying a quasi-static load is different from those that result from applying a cyclic load.

Estimating the pressure force around swimming plankton using micro particle image velocimetry

Obtaining pressure force for freely swimming microorganisms is a challenging yet important problem. Here, we report the swimming kinematics and dynamics of the zooplankton Acartia tonsa nauplius investigated using Micro Particle Image Velocimetry (µPIV). Using rigid object tracking, we obtain sub-pixel accurate localization of freely swimming A. tonsa, revealing its highly periodic locomotion. We exploit this periodicity to obtain phase-locked averaged kinematics for position, speed, and acceleration. The swimming speed profile of A. tonsa has a distinct double peak, due to its two power strokes. Next, we investigate the flow field around swimming A. tonsa using µPIV. We dynamically mask A. tonsa in µPIV images using an object-fixed coordinate transformation, leveraging the sub-pixel accurate localization. Our analysis shows of a pair of attached vortices during the two power strokes, which are pushed away during the recovery stroke. Finally, using a semi-implicit pressure velocity algorithm, we calculate the pressure force from the time-dependent flow fields. These calculations indicate a low-pressure region ahead of the A. tonsa during the peak of the power strokes. The vertical pressure force correlates well with the vertical swimming speed.

Grain boundary effects in high-temperature liquid-metal dealloying: a multi-phase field study

A multi-phase field model is employed to study the microstructural evolution of an alloy undergoing liquid dealloying, specifically considering the role of grain boundaries. A semi-implicit time-stepping algorithm using spectral methods is implemented, which enables simulating large 2D and 3D domains over long time scales while still maintaining a realistic interfacial thickness. Simulations reveal a mechanism of coupled grain–boundary migration to maintain equilibrium contact angles with the topologically complex solid–liquid interface, which locally accelerates diffusion-coupled growth of a liquid channel into the precursor. This mechanism asymmetrically disrupts the ligament connectivity of the dealloyed structure in qualitative agreement with published experimental observations. The grain boundary migration-assisted corrosion channels form even for precursors with small amounts of the dissolving alloy species, below the parting limit. The activation of this grain boundary dealloying mechanism depends strongly on grain boundary mobility.

Fluid dynamic and thermal performance of a slotted cylinder at low Reynolds number

The fluid dynamic and thermal performance of a circular cylinder with a slot parallel to the flow is numerically investigated. The study utilized the semi-implicit finite volume multi-material algorithm MPM-ICE, a component of the Uintah framework. The normalized slot width s/D ranges from 0.1 - 0.3, introducing an additional heat transfer surface area between ∼ 10 and ∼ 50%, and a mass reduction between ∼ 13 and ∼ 38% in the cylinder. We assumed two-dimensional incompressible flow and simulated a Reynolds number ReD between 100 and 1000. The slotted cylinders are found to have a total drag force reduction up to ∼ 45%, compared to a solid cylinder despite the additional viscous drag force in the slot. Convection heat transfer is enhanced up to ∼ 70%. The slotted cylinder performance index, defined as the ratio of the heat rate to the drag force, increases up to maximum of ∼ 3, indicating better overall thermal fluid performance. An entropy analysis showed the best performance index occurs at the highest ReD. Correlations for drag coefficient and Nusselt number are proposed along with an entropy optimization method.

A new micromechanical damage model for quasi-brittle geomaterials with non-associated and state-dependent friction law

In this paper, we shall present a new micromechanical damage model for capturing the mechanical behaviors of quasi-brittle geomaterials under a wide range of compressive stress. Two essential coupled non-linear mechanisms are taken into account: plastic deformation related to frictional sliding along the microcrack surfaces, and microscopic damage induced by the initiation and propagation of microcracks. Within the framework of thermodynamics and Mori–Tanaka homogenization scheme, free energy and thermodynamic forces, including the local stress applied on the microcracks and damage driving force are deduced. The main novelty of this work lies in presenting a new physically based non-associated and state-dependent friction law to capture the plastic distortion, in which the friction coefficient is no longer a constant but a state-dependent variable varying with the surface asperities of microcracks. The relationship between the friction coefficient and mean local stress, as well as microscopic damage is subtly defined. Intriguingly, a macroscopic strength criterion is derived as an inherent part of the proposed model without rotation of the principal stress. Moreover, semi-analytical stress–strain–damage relationships of the proposed model can be derived under conventional triaxial compression. These up-scaling analyses provide a powerful tool for parameter calibration. For application, the semi-implicit return mapping algorithm with plasticity-damage decoupling correction procedure (SRM-PDDC) is adopted for numerical implementation. To demonstrate the performance of the micromechanical model, we compare the model predictions with experimental data of quasi-brittle rocks in literature as well as the results obtained by Zhu et al. (2016). Finally, the applicable condition of the SRM-PDDC algorithm is discussed in detail.

An edge-based smoothed finite element method for semi-implicit coupling of unsteady viscoelastic fluid–structure interaction

In this paper, a new partitioned semi-implicit coupling algorithm is developed for unsteady viscoelastic fluid–structure interaction in association with an edge-based smoothed finite element method (ESFEM). Stabilization techniques tailored for the viscoelastic fluid subproblem are naturally integrated into the hybrid explicit/implicit coupling framework to achieve the enhanced stability. In particular, a mass source term derived from the modified continuity equation in the finite-element context enables the ESFEM to fulfill the geometric conservation law on variable-node smoothing cells during the subiterations. Moreover, both multi-field equations and interface conditions are easily discretized with the ESFEM which enjoys high flexibility of smoothed Galerkin weak-form integral. Desirable numerical results are given for two benchmark problems.

Numerical Investigation of Natural Convention to a Pseudoplastic Fluid in a Long Channel using a Semi-Implicit Scheme

We develop and computationally analyze a mathematical model for natural convection to a non-Newtonian fluid in a long and thin channel. The channel is bounded by antisymmetric heated and cooled walls and encloses a non-Newtonian pseudoplastic fluid. The flow and heat transfer characteristics are investigated subject to the prevailing buoyancy forces resulting from the combined natural convection and gravitational effects. An efficient and accurate semi-implicit finite difference algorithm is implemented in time and space to analyse the model equations. In the case when the fluid flow and heat transfer are sustained for a long enough time to allow for steady states to develop, the model equations would reduce to a boundary value problem. Even in such cases, we demonstrate that, by recasting the problem as an initial boundary value problem, our numerical algorithms would still converge in time to the relevant, steady-state solutions of the original boundary value problem. We also demonstrate the dependence of solutions on the embedded parameters at a steady state.

A semi-implicit slip algorithm for mesh deformation in complex geometries, implemented in OpenFOAM

Many engineering applications of computational fluid dynamics (CFD) comprise extensive movement of objects that necessitate complex dynamic mesh treatments. In particular, the mesh motion process frequently requires a proper slipping of mesh points on highly curved surfaces. The currently available implementation of explicit slip boundary conditions in OpenFOAM fails to allow large deformations of the mesh without severely degrading the mesh quality and inverting some of the cells. Thus, a robust semi-implicit slip algorithm, based on the Laplacian smoothing methodology, is developed in the present work to tackle this issue. The algorithm is in fact performed in two steps, one explicit and one implicit. The OpenFOAM implementation of the algorithm includes different mesh motion solvers and boundary conditions, based on the displacement or velocity of points. The method is first verified using simple, yet relevant, test cases, and it is shown that the developed algorithm significantly outperforms some of the well-known proprietary CFD codes. Then, it is applied to a complex practical CFD case study. An engineering application that requires the features of the developed mesh motion algorithm is the transient operation of Kaplan turbines. These double-regulated machines simultaneously adjust the guide vane and runner blade angles while changing the operating condition. CFD simulations of such transient operations are highly complex, as they involve mesh deformation of the guide vane passage and simultaneous mesh deformation and rigid-body rotation of the runner blade passage. The mesh deformation requires points to slip on the curved hub and shroud surfaces while preserving the cell quality in tiny blade clearances. Therefore, the feasibility of the developed algorithm is evaluated for a load rejection sequence of a Kaplan turbine model. Program summaryProgram Title: Semi-implicit slip mesh motionCPC Library link to program files:https://doi.org/10.17632/wztc26vh7b.1Developer's repository link:https://github.com/salehisaeed/semiImplicitSlipLicensing provisions: GPLv3Programming language: C++Nature of problem: CFD simulations of numerous engineering fluid flows, such as transient operation of hydraulic turbines, involve an immensely complicated mesh motion process consisting of simultaneous mesh deformation and mesh slipping on highly curved surfaces. The available standard mesh motion methodology in OpenFOAM lacks some features to simulate this elaborate mesh motion. The introduced program addresses this problem by developing a new dynamic mesh algorithm.Solution method: The program implements a robust semi-implicit algorithm for slipping the mesh points on curved surfaces. The algorithm includes two steps, namely, an explicit step based on the general slip condition and an implicit step based on the Dirichlet condition. It employs the Laplacian smoothing equations to spread the mesh deformation into the domain. Additionally, a solid-body rotation may be added on top of the deformed mesh, which could be useful for modeling the runner region in transient operation of Kaplan turbines which contains simultaneous mesh deformation and solid-body rotation of the mesh.

An improved fractional-step method on co-located unstructured meshes for weakly compressible flow simulations

A pressure-based semi-implicit algorithm on the cell-centered unstructured mesh with co-located variable arrangement has been developed to efficiently and robustly calculate the low-Mach number variable-density flows, where thermal dilatation is important. The proposed fractional-step method follows the conventional operator-splitting procedure, but is incorporated with several improvements. Instead of the traditional Poisson equation, the Helmholtz equation is formulated for the pressure correction. The finite-volume method with second-order accuracy in space is used to discretize the governing equations. Numerical tests justify the effectiveness and robustness of this improved algorithm.

Numerical simulation of two-dimensional biomagnetic shear flow

The current work focuses on numerical analysis of two-dimensional simple shear flow of biomagnetic fluid flowing in the vicinity of non-uniform magnetic field. Accordingly, the numerical model is constructed with the help of semi-implicit fractional step algorithm utilizing a finite volume method to solve the corresponding continuity and Navier-Stokes equations. Numerical simulations are mainly focussed on changing Reynolds number (Re), magnetic number (Mn) and Stuart number(N). The results reveal that multiple recirculation zones emerge as a result of the combined influence of flow and magnetic field. Out of the three parameters considered, the formation of vortices is not affected by variation of Stuart number compared to Reynolds and magnetic numbers.

효율적인 저마하수 유동 음향 포착을 위한 OpenFOAM 기반의 압력기반 압축성 해석자 분석

For efficient capturing of low-Mach flow acoustics, a compressible pressure-based semi-implicit algorithm with characteristic splitting is implemented on the OpenFOAM framework. In this paper, detailed descriptions of the OpenFOAM code for SICS algorithms were shown and a comparison study of semi-implicit characteristic splitting (SICS) and compressible PIMPLE algorithm was performed. To validate SICS solver, the aeolian tone of the cylinder was simulated and the corresponding acoustic pressure was compared with the previously reported value. To evaluate pressure-based solver performance, acoustic wave propagation and scattering problems were simulated. It is found that a pressure-based solver with SICS algorithm shows better cost-effective performance on low-Mach flow acoustics than a solver with a compressible PIMPLE algorithm. The present SICS solver was extended to reacting flow and one-dimensional flame structures were resolved correctly. The SICS solver can be used to simulate flame-acoustic coupling of low-Mach flow more efficiently.

Geometric consistent fuzzy cluster ensemble with membership reconstruction for image segmentation

In recent years, to handle the ubiquitous uncertainty and unknown noise, different fuzzy clustering methods have been introduced to solve image segmentation problem for various applications, such as natural image, satellite image, multichannel (typically remote sensing) image. In fact, it is hard to know which one is the best for specified task. Cluster ensemble method is proposed to solve the problem of choosing a particular fuzzy clustering algorithm, or a special image processing before clustering, that best suits the given image segmentation task. In fuzzy cluster ensemble, membership vectors generated from different fuzzy clustering methods are merged into one vector as an input object, which is also a combination of data partitions. However, this kind of input object may lose detail information from original target image and may cause inaccurate edges in segmentation results. Moreover, by means of treating it as a new representation of original data, the membership vector of fuzzy cluster ensemble should be intuitively geometric consistent with the original target image. In this paper, by holding this view, we develop a geometric consistent fuzzy cluster ensemble model for spatial data, which involves a constraint between the membership and its reconstruction, to improve the clustering performance on image segmentation. In the proposed model, a pre-determined gradient-preserving weight is used in the membership reconstruction item to make the membership matrix be geometric consistent with the original target image. A semi-implicit optimization iterative algorithm is adopted to solve the proposed geometric consistent model. Experimental results demonstrate the effectiveness of proposed model in synthetic and real-world image segmentation problems over several state-of-the-art methods.

A semi-implicit meshless method for incompressible flows in complex geometries

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions (RBF) as interpolants. Higher-order polynomials are appended to the polyharmonic splines (PHS-RBF) and a collocation method is used to derive the interpolation coefficients. The interpolating kernels are then differentiated and the partial-differential equations are satisfied by collocation at the scattered points. The PHS-RBF interpolation is shown to be exponentially convergent with discretization errors decreasing as a high power of a representative distance between points. We present here a semi-implicit algorithm for time-dependent and steady state fluid flows in complex domains. At each time step, several iterations are performed to converge the momentum and continuity equations. A Poisson equation for pressure corrections is formulated by imposing divergence free condition on the iterated velocity field. At each time step, the momentum and pressure correction equations are repeatedly solved until the velocities and pressure converge to a pre-specified tolerance. We have demonstrated the convergence and discretization accuracy of the algorithm for two model problems and simulated four other complex problems. In all cases, the algorithm is stable for Courant numbers in excess of ten. The algorithm has the potential to accurately and efficiently solve many fluid flow and heat transfer problems in complex domains. An open source code Meshless Multi-Physics Software (MeMPhyS) [1] is available for interested users of the algorithm.

A Computational Model for Nonlinear Biomechanics Problems of FGA Biological Soft Tissues

The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlinear bio-thermal stress distributions in functionally graded anisotropic biological tissues. Numerical findings verified the validity, accuracy, and efficiency of the proposed method.

A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior

A dynamic coupled elastoplastic damage model for rock-like materials is proposed. The model takes unified strength theory as the strength criterion. To characterize the different damage between compression and tension, two damage variables both in compression and in tension are introduced into the model. The former is represented by the generalized shear plastic strain and volumetric plastic strain and the latter is expressed with the generalized shear plastic strain. Furthermore, the model takes the strain rate effect into account to reflect the strength enhancement under dynamic loading. Because of the difference in plastic hardening between compression and tension, a modified hardening function is adopted. At the same time, the volume strain from HJC model is modified to be consistent with one of continuum mechanics. The developed model is numerically implemented into LS-DYNA with a semi-implicit algorithm through a user-defined material interface (UMAT). The reliability and accuracy of the developed model are verified by the simulation of four basic experiments with different loading conditions. The proposed model was found to be applicable to different mechanical behaviors of rock-like materials under static and dynamic loading conditions.