Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using near-wall modelling

We present a validation strategy for enhancement of an unstructured industrial finite-volume solver designed for steady RANS problems for large-eddy-type simulation with near-wall modelling of incompressible high Reynolds number flow. Different parts of the projection-based discretisation are investigated to ensure LES capability of the numerical method. Turbulence model parameters are calibrated by using a minimisation of least-squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow. Then the method is applied to the flow over a backward facing step at Re_h = 37,500. Of special interest is the role of the spatial and temporal discretisation error for low order schemes. For wall-bounded flows, present results confirm existing best practice guidelines for mesh design. For free-shear layers, a sensor to quantify the resolution quality of the LES based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at Re_h = 37,500.     

Extension of a hybrid thermal LBE scheme for large-eddy simulations of turbulent convective flows

Following the work of Lallemand and Luo [Lallemand P, Luo L-S. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 2003;68:036706] we validate, apply and extend the hybrid thermal lattice Boltzmann scheme (HTLBE) by a large-eddy approach to simulate turbulent convective flows. For the mass and momentum equations, a multiple-relaxation-time LBE scheme is used while the heat equation is solved numerically by a finite difference scheme. We extend the hybrid model by a Smagorinsky subgrid scale model for both the fluid flow and the heat flux. Validation studies are presented for laminar and turbulent natural convection in a cavity at various Rayleigh numbers up to 5 × 10¹⁰ for Pr = 0.71 using a serial code in 2D and a parallel code in 3D, respectively. Correlations of the Nusselt number are discussed and compared to benchmark data. As an application we simulated forced convection in a building with inner courtyard at Re = 50 000.     

Unsteady development of a deformable bubble rising in a quiescent liquid

An accurate finite-volume based numerical method for the simulation of an isothermal two-phase flow, consisting of a rising deformable bubble translating in a quiescent, unbounded liquid, is presented. This direct simulation method is built on a sharp interface concept and developed on an Eulerian, Cartesian fixed-grid with a cut-cell scheme and marker points to track the moving interface. The unsteady Navier–Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true surface phase boundary to determine the evolving interface shape and movement of the bubble. The highlights of this method are that it utilizes a combined Eulerian–Lagrangian approach, and is capable of treating the interface as a sharp discontinuity. A fixed underlying grid is used to represent the control volume. The interface, however, is denoted by a separate set of marker particles which move along with the interface. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. This numerical scheme can handle a wide range of density and viscosity ratios. The bubble is assumed to be spherical and at rest initially, but deforms as it rises through the liquid pool due to buoyancy. Additionally, the flow is assumed to be axisymmetric and incompressible. The bubble deformation and dynamic motion are characterized by the Reynolds number, the Weber number, the density ratio and the viscosity ratio. The effects of these parameters on the translational bubble dynamics and shape are given and the physical mechanisms are explained and discussed. Results for the shape, velocity profile and various forces acting on the bubble are presented here as a function of time until the bubble reaches terminal velocity. The range of Reynolds numbers investigated is 1 < Re < 100, and that of Weber number is 1 < We < 10.     

Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook–White equation, is presented. An extensive comparison test was established on the 20 × 500 grid, for a wide range of relative roughness (ε/D) and Reynolds number (R) values (1 × 10^?6 ? ε/D ? 5 × 10^?2; 4 × 10³ ? R ? 10⁸), covering a large portion of turbulent flow zone in Moody’s diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of ε/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 5 × 10^?4, a maximum absolute error of 4 × 10^?3 whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of ε/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of ε/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.     

Simulation of constituent transport using a reduced 3D constituent transport model (CTM) driven by HF Radar: Model application and error analysis

Data-driven constituent transport models (CTM), which take surface current measurements from High Frequency (HF) Radar as input can be applied within the context of real-time environmental monitoring, oceanographic assessment, response to episodic events, as well as search and rescue in surface waters.This paper discusses a numerical method that allows for the evaluation of diffusion coefficients in anisotropic flow fields from surface current measurements using HF Radar. The numerical scheme developed was incorporated into a data-driven CTM and through model error analyses, the effects of using spatially variable transport coefficients on model predictions were examined. The error analyses were performed on the model by varying the cell Reynolds number, Re = f(u,K,Δx) between 0.15 and 100, where u is the velocity vector within the flow field, K is a diffusivity tensor and Δx is the computational grid cell size.Two instantaneous releases of conservative material were then modeled, the model being initialized at two different locations within the domain. From the two simulation runs, marked differences in the predicted spatial extent of the conservative material resulting from the spatially varying diffusivity values within the study area were observed. Model predictions in terms of variance or size estimates of a diffusing patch were found to be more affected from using inaccurate diffusivity estimates, and less affected from using inaccurate current measurements. The largest errors occurred at Re > 2 associated with changing diffusivity values, going up to as much as a 25-fold difference in variance estimates at Re = 100. Very little effect on variance estimates due to varying velocity values were observed even at Re > 2. This model was applied within the framework of constituent tracking to Corpus Christi Bay in the Texas Gulf of Mexico region.     

Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements

A variational multiscale large-eddy simulation (VMS-LES) code, named MISTRAL, has been developed based upon the finite element method (FEM) for accurate and practical computation of geometrically complicated turbulent flow problems. The numerical strategy of the FEM-based VMS-LES is explained, especially focusing on the double-scale approximation for velocity and pressure in the incompressible Navier-Stokes equations, a pressure stabilization technique and a multiscale turbulence modeling. A unique technique is also employed in the time integration to realize an efficient inversion of the multiscale mass matrix and to form the multiscale pressure Poisson equation used in the approximate projection method for divergence-free constraint of velocity. As a numerical demonstration, a 2D driven cavity flow problem has been solved with the MISTRAL code in a wide range of Reynolds number (Re=1000 to 50000). The results are compared with reference data to quantitatively estimate the accuracy (magnitude of errors in terms of L ² norms) of the proposed VMS-LES method.     

Performance analysis of networks of queues under active queue management scheme

Analysis of networks of queues under repetitive service blocking mechanism has been presented in this paper. Nodes are connected according to an arbitrary configuration and each node in the networks employs an active queue management (AQM) based queueing policy to guarantee certain quality of service for multiple class external traffic. This buffer management scheme has been implemented using queue thresholds. The use of queue thresholds is a well known technique for network traffic congestion control. The analysis is based on a queue-by-queue decomposition technique where each queue is modelled as a GE/GE/1/N queue with single server, R (R ⩾ 2) distinct traffic classes and {N = N₁, N₂, … , N_R} buffer threshold values per class under first-come-first-serve (FCFS) service rule. The external traffic is modelled using the generalised exponential (GE) distribution which can capture the bursty property of network traffic. The analytical solution is obtained using the maximum entropy (ME) principle. The forms of the state and blocking probabilities are analytically established at equilibrium via appropriate mean value constraints. The initial numerical results demonstrate the credibility of the proposed analytical solution.     

Guaranteed-quality all-quadrilateral mesh generation with feature preservation

In this paper, a quadtree-based mesh generation method is described to create guaranteed-quality, geometry-adapted all-quadrilateral (all-quad) meshes with feature preservation for arbitrary planar domains. Given point cloud, our method generates all-quad meshes with these points as vertices and all the angles are within [45°, 135°]. For given planar curves, quadtree-based spatial decomposition is governed by the curvature of the boundaries and narrow regions. 2-refinement templates are chosen for local mesh refinement without creating any hanging nodes. A buffer zone is created by removing elements around the boundary. To guarantee the mesh quality, the angles facing the boundary are improved via template implementation, and two buffer layers are inserted in the buffer zone. It is proved that all the elements of the final mesh are quads with angles between 45° ± ε and 135° ± ε (ε ≤ 5°) with the exception of badly shaped elements that may be required by the sharp angles in the input geometry. We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin(45° ? ε), sin90°], or [0.64, 1.0]. Furthermore, sharp features and narrow regions are detected and preserved automatically. Boundary layer meshes are generated by splitting elements of the second buffer layer. We have applied our algorithm to a set of complicated geometries, including the Lake Superior map and the air foil with multiple components.     

Coarse-Grained Parallel Geometric Search

We present a parallel algorithm for solving thenext element search problemon a set of line segments, using a BSP-like model referred to as thecoarse grained multicomputer(CGM). The algorithm requiresO(1) communication rounds (h-relations withh=O(n/p)),O((n/p) log n) local computation, andO((n/p) log p) memory per processor, assumingn/p⩾p. Our result implies solutions to the point location, trapezoidal decomposition, and polygon triangulation problems. A simplified version for axis-parallel segments requires onlyO(n/p) memory per processor, and we discuss an implementation of this version. As in a previous paper by Develliers and Fabri (Int. J. Comput. Geom. Appl.6(1996), 487–506), our algorithm is based on a distributed implementation of segment trees which are of sizeO(n log n). This paper improves onop. cit.in several ways: (1) It studies the more general next element search problem which also solves, e.g., planar point location. (2) The algorithms require onlyO((n/p) log n) local computation instead ofO(log p*(n/p) log n). (3) The algorithms require onlyO((n/p) log p) local memory instead ofO((n/p) log n).     

Domain decomposition based coupling between the lattice Boltzmann method and traditional CFD methods – Part II: Numerical solution to the backward facing step flow

The lattice Boltzmann method (LBM) and traditional finite difference methods have separate strengths when solving the incompressible Navier–Stokes equations. The LBM is an explicit method with a highly local computational nature that uses floating-point operations that involve only local data and thereby enables easy cache optimization and parallelization. However, because the LBM is an explicit method, smaller grid spacing requires smaller numerical time steps during both transient and steady state computations. Traditional implicit finite difference methods can take larger time steps as they are not limited by the CFL condition, but only by the need for time accuracy during transient computations. To take advantage of the strengths of both methods, a multiple solver, multiple grid block approach was implemented and validated for the 2-D Burgers’ equation in Part I of this work. Part II implements the multiple solver, multiple grid block approach for the 2-D backward step flow problem. The coupled LBM–VSM solver is found to be faster by a factor of 2.90 (2.87 and 2.93 for Re = 150 and Re = 500, respectively) on a single processor than the VSM for the 2-D backward step flow problem while maintaining similar accuracy.     

Simulation of solid thermal explosion and liquid thermal explosion of dicumyl peroxide using calorimetric technique

Dicumyl peroxide (DCPO), is produced by cumene hydroperoxide (CHP) process, is utilized as an initiator for polymerization, a prevailing source of free radicals, a hardener, and a linking agent. DCPO has caused several thermal explosion and runaway reaction accidents in reaction and storage zone in Taiwan because of its unstable reactive property. Differential scanning calorimetry (DSC) was used to determine thermokinetic parameters including 700 J g^–1 of heat of decomposition (ΔH_d), 110 °C of exothermic onset temperature (T₀), 130 kJ mol^–1 of activation energy (E_a), etc., and to analyze the runaway behavior of DCPO in a reaction and storage zone. To evaluate thermal explosion of DCPO with storage equipment, solid thermal explosion (STE) and liquid thermal explosion (LTE) of thermal safety software (TSS) were applied to simulate storage tank under various environmental temperatures (T_e). T_e exceeding the T₀ of DCPO can be discovered as a liquid thermal explosion situation. DCPO was stored under room temperature without sunshine and was prohibited exceeding 67 °C of self-accelerating decomposition temperature (SADT) for a tank (radius = 1 m and height = 2 m). SADT of DCPO in a box (width, length and height = 1 m, respectively) was determined to be 60 °C. The TSS was employed to simulate the fundamental thermal explosion behavior in a large tank or a drum. Results from curve fitting demonstrated that, even at the earlier stage of the reaction in the experiments, ambient temperature could elicit exothermic reactions of DCPO. To curtail the extent of the risk, relevant hazard information is quite significant and must be provided in the manufacturing process.     

On the influence of the number of algorithms,problems, and independent runs in the comparison of evolutionary algorithms

When conducting a comparison between multiple algorithms on multiple optimisation problems it is expected that the number of algorithms, problems and even the number of independent runs will affect the final conclusions. Our question in this research was to what extent do these three factors affect the conclusions of standard Null Hypothesis Significance Testing (NHST) and the conclusions of our novel method for comparison and ranking the Chess Rating System for Evolutionary Algorithms (CRS4EAs). An extensive experiment was conducted and the results were gathered and saved of k = 16 algorithms on N = 40 optimisation problems over n = 100 runs. These results were then analysed in a way that shows how these three values affect the final results, how they affect ranking and which values provide unreliable results. The influence of the number of algorithms was examined for values k = {4, 8, 12, 16}, number of problems for values N = {5, 10, 20, 40}, and number of independent runs for values n = {10, 30, 50, 100}. We were also interested in the comparison between both methods – NHST's Friedman test with post-hoc Nemenyi test and CRS4EAs – to see if one of them has advantages over the other. Whilst the conclusions after analysing the values of k were pretty similar, this research showed that the wrong value of N can give unreliable results when analysing with the Friedman test. The Friedman test does not detect any or detects only a small number of significant differences for small values of N and the CRS4EAs does not have a problem with that. We have also shown that CRS4EAs is an appropriate method when only a small number of independent runs n are available.     

Some Applications of Magma in Designs and Codes: Oval Designs,Hermitian Unitals and Generalized Reed–Muller Codes

We describe three applications of Magma to problems in the area of designs and the associated codes:  •  Steiner systems, Hadamard designs and symmetric designs arising from an oval in an even-order plane, leading in the classical case to bent functions and difference-set designs;  •  the Hermitian unital as a 2-(q³ +  1, q +  1, 1) design, and the code overF_p where p divides q +  1;  •  a basis of minimum-weight vectors for the code over F_pof the design of points and hyperplanes of the affine geometry AG_d(F_p), where p is a prime.     

Gröbner Bases Applied to Finitely Generated Field Extensions

Using a constructive field-ideal correspondence it is shown how to compute the transcendence degree and a (separating) transcendence basis of finitely generated field extensionsk (x) / k(g), resp. how to determine the (separable) degree if k(x) / k(g) is algebraic. Moreover, this correspondence is used to derive a method for computing minimal polynomials and deciding field membership. Finally, a connection between certain intermediate fields of k(x) / k(g) and a minimal primary decomposition of a suitable ideal is described. For Galois extensions the field-ideal correspondence can also be used to determine the elements of the Galois group.     

Primary Decomposition of Lattice Basis Ideals

We study the primary decomposition of lattice basis ideals. These ideals are binomial ideals with generators given by the elements of a basis of a saturated integer lattice. We show that the minimal primes of such an ideal are completely determined by the sign pattern of the basis elements, while the embedded primes are not. As a special case we examine the ideal generated by the 2  ×  2 adjacent minors of a generic m × n matrix. In particular, we determine all minimal primes in the 3  × n case. We also present faster ways of computing a generating set for the associated toric ideal from a lattice basis ideal.     

Numerical modeling of interaction of a current with a circular cylinder near a rigid bed

The numerical modeling of 2D turbulent flow around a smooth horizontal circular cylinder near a rigid bed with gap ratio G/D = 0.3 at Reynolds number Re_D = 9500 is investigated. Ansys^® 10.0-FLOTRAN program package is used to solve the governing equations by FEM, and the performance of the standard k ? ε, standard k ? ω, and SST turbulence models are examined. A sensitivity study for the three turbulence models is carried out on three computational meshes with different densities near the cylinder surface. The computational velocity fields and the Strouhal numbers from the present simulations are compared with those obtained from the PIV measurement. It is found that the time-averaged velocity field of the flow in the proximity of the cylinder is closely affected by the mesh resolution near the cylinder surface, and the mesh refinement in radial direction improves the results of present simulations. The shedding of vortices in the cylinder wake is not predicted by k ? ε model on all the three meshes. The results for the time-averaged velocity field show that the numerical modeling using either of k ? ω and SST turbulence models on the finest mesh used on the cylinder surface is reasonably successful.     

Factors responsible for the aggregation behavior of hydrophobic polyelectrolyte PEA in aqueous solution studied by molecular dynamics simulations

Self-association (i.e. interchain aggregation) behavior of atactic poly(ethacrylic acid) PEA in dilute aqueous solution as function of degree-of-neutralization by Na⁺ counter-ions (i.e. charge fraction f) was investigated by molecular dynamics simulations. Aggregation is found to occur in the range 0 ≤ f ≤0.7 in agreement with experimental results compared at specified polymer concentration C_p = 0.36 mol/l in dilute solution. The macromolecular solution was characterized and analysed for radius-of-gyration, torsion angle distribution, inter and intra-molecular hydrogen bonds, radial distribution functions of intermolecular and inter-atomic pairs, inter-chain contacts and solvation enthalpy. The PEA chains form aggregate through attractive inter-chain interaction via hydrogen bonding, in the range f < 0.7, in agreement with experimental observation. The numbers of inter-chain contacts decreases with f. A critical structural transition occurs at f = 0.7, observed via simulations for the first time, in R_g as well as inter-chain H-bonds. The inter-chain distance increases with f due to repulsive interactions between COO− groups on the chains. PEA-PEA electrostatic interactions dominant solvation enthalpy. The PEA solvation enthalpy becomes increasingly favorable with increase in f. The transition enthalpy change, in going from uncharged (acid) state to fully charged state (f = 1) is unfavorable towards aggregate formation.     

On identifying codes that are robust against edge changes

Assume that G = (V, E) is an undirected graph, and C ⊆ V. For every v ∈ V, denote I_r(G; v) = {u ∈ C: d(u,v) ≤ r}, where d(u,v) denotes the number of edges on any shortest path from u to v in G. If all the sets I_r(G; v) for v ∈ V are pairwise different, and none of them is the empty set, the code C is called r-identifying. The motivation for identifying codes comes, for instance, from finding faulty processors in multiprocessor systems or from location detection in emergency sensor networks. The underlying architecture is modelled by a graph. We study various types of identifying codes that are robust against six natural changes in the graph; known or unknown edge deletions, additions or both. Our focus is on the radius r = 1. We show that in the infinite square grid the optimal density of a 1-identifying code that is robust against one unknown edge deletion is 1/2 and the optimal density of a 1-identifying code that is robust against one unknown edge addition equals 3/4 in the infinite hexagonal mesh. Moreover, although it is shown that all six problems are in general different, we prove that in the binary hypercube there are cases where five of the six problems coincide.     

Tetrel bonds between PySiX3 and some nitrogenated bases: Hybridization,substitution, and cooperativity

Ab initio calculations have been performed to study the influence of hybridization, substitution, and cooperativity on the tetrel bond in the complexes of PySiX₃ (Py = pyridine and X = halogen). The tetrel bond becomes stronger in the order of p-PySiF₃⋯NCH(sp) < p-PySiF₃⋯NHCH₂(sp²) < p-PySiF₃⋯NH₃(sp³). The electron-donating group in the electron donor strengthens the tetrel bond, and this effect is mainly achieved through electrostatic and polarization interactions. Tetrel bonding displays cooperative effects with triel bonding and chalcogen bonding, characterized by shorter binding distances and greater electron densities. The cooperative effects between triel/chalcogen bond and tetrel bond have been analyzed by molecular electrostatic potentials and charge transfer. Energy decomposition indicates that many-body effects are mainly caused by polarization energy. The geometries of Si⋯N interaction and its applications in crystal materials have been characterized and evidenced by a CSD research.     

A study of nonlinear dispersive equations with solitary-wave solutions having compact support

With the use of Adomian decomposition method, the prototypical, genuinely nonlinear K(m,n) equation, u_t+(u^m)_x+(uⁿ)_xxx=0, which exhibits compactons — solitons with finite wavelength — is solved exactly. Two numerical illustrations, K(2,2) and K(3,3), are investigated to illustrate the pertinent features of the proposed scheme. The technique is presented in a general way so that it can be used in nonlinear dispersive equations.