Mesh Scale Research Articles

A RANS model correction on unphysical over-prediction of turbulent quantities across shock wave

The unphysical increase of turbulent quantities in turbulence model induced by shock wave in simulations of hypersonic flows and its influence on the aerothermal prediction are studied. Using k-ω SST model, numerical experiments on the hypersonic flow over a blunt body indicate that the strong detached shock wave will result in serious unphysical increase of turbulent quantities and the increase magnitudes are closely related to the mesh scales near the shock wave. This phenomenon could generally cause an over-prediction of the aerothermal prediction. To eliminate this unphysical phenomenon and enhance the accuracy of aerothermal prediction, a new correction model for current k-ω SST model is established, which includes two parts: a shock wave detector to identify the location of shock wave and a damping function for the production terms in turbulent transport equations. Finally, the modified k-ω SST model using the correction model is applied to two types of hypersonic flows. Numerical results prove that the correction model can effectively eliminate the unphysical increase of turbulent quantities around the shock wave and meanwhile does not affect the normal development of turbulent quantities inside boundary layer. Through the correction model, the accuracy of aerothermal prediction is remarkably improved.

Designing hydrogels for controlled drug delivery.

Hydrogel delivery systems can leverage therapeutically beneficial outcomes of drug delivery and have found clinical use. Hydrogels can provide spatial and temporal control over the release of various therapeutic agents, including small-molecule drugs, macromolecular drugs and cells. Owing to their tunable physical properties, controllable degradability and capability to protect labile drugs from degradation, hydrogels serve as a platform in which various physiochemical interactions with the encapsulated drugs control their release. In this Review, we cover multiscale mechanisms underlying the design of hydrogel drug delivery systems, focusing on physical and chemical properties of the hydrogel network and the hydrogel-drug interactions across the network, mesh, and molecular (or atomistic) scales. We discuss how different mechanisms interact and can be integrated to exert fine control in time and space over the drug presentation. We also collect experimental release data from the literature, review clinical translation to date of these systems, and present quantitative comparisons between different systems to provide guidelines for the rational design of hydrogel delivery systems.

Occurring mechanism and restraining method research of numerical noise signal in penetration simulation

In hard target penetration simulation, the existing researches of the convergence of results are mainly concentrating in the corresponding relationship between penetration depth and mesh scales. However, the influence of the mesh difference on the penetration resistance and acceleration signals are seldom refer to. This paper presents the occurring mechanism and restraining method of numerical noise signal in penetration simulation. First, the concept of the noise signal izs proposed. By taking a 3D penetration simulation as example, the influence of the noise signal on the penetration resistance in different mesh scales and impact velocity is studied. To ensure the convergence of the computational results, the grid scale of the target is encrypted to 1:1:8. In addition, modern spectrum analysis method is introduced to further analyze the penetration resistance signal. The research results presented is useful to improve the computational accuracy of high speed projectile penetration simulation, and provide important reference for carrying out structural design and optimization of fuze system.

Modelling VARTM process induced variations on bending performance of composite Omega beams

Finite element simulation with cohesive contact is presented, to correlate the vacuum assisted RTM process and the bending performance of Omega beams. The model considers the process induced variations, including part thickness, resin rich pockets and voids. The bending performance prediction relies on cohesive contact to model delamination initiation and propagation. Computing efficiency is achieved by mesh scaling. The modelling approach applies to three variations of Omega beams with the different mode-mixture ratios. The finite element predictions result in a high degree of agreement with the experimental measurements.

Mesh Scaling for Affordable Solution Verification

Solution verification is the process of verifying the solution of a finite element analysis by performing a series of analyses on meshes of increasing mesh densities, to determine if the solution is converging. Solution verification has historically been too expensive, relying upon refinement templates resulting in an 8X multiplier in the number of elements. For even simple convergence studies, the 8X and 64X meshes must be solved, quickly exhausting computational resources. In this paper, we introduce Mesh Scaling, a new global mesh refinement technique for building series of all-hexahedral meshes for solution verification, without the 8X multiplier. Mesh Scaling reverse engineers the block decomposition of existing all-hexahedral meshes followed by remeshing the block decomposition using the original mesh as the sizing function multiplied by any positive floating number (e.g. 0.5X, 2X, 4X, 6X, etc.), enabling larger series of meshes to be constructed with fewer elements, making solution verification tractable.

Two‐level consistent splitting methods based on three corrections for the time‐dependent Navier–Stokes equations

SummaryThree kinds of two‐level consistent splitting algorithms for the time‐dependent Navier–Stokes equations are discussed. The basic technique of two‐level type methods for solving the nonlinear problem is first to solve a nonlinear problem in a coarse‐level subspace, then to solve a linear equation in a fine‐level subspace. Hence, the two‐level methods can save a lot of work compared with the one‐level methods. The approaches to linearization are considered based on Stokes, Newton, and Oseen corrections. The stability and convergence demonstrate that the two‐level methods can acquire the optimal accuracy with the proper choice of the coarse and fine mesh scales. Numerical examples show that Stokes correction is the simplest, Newton correction has the best accuracy, while Oseen correction is preferable for the large Reynolds number problems and the long‐time simulations among the three methods. Copyright © 2015 John Wiley & Sons, Ltd.

Modelling Dam Break Evolution over a Wet Bed with Smoothed Particle Hydrodynamics: A Parameter Study

When investigating water flow in spillways and energy dissipation, it is important to know the behavior of the free surfaces. To capture the real dynamic behavior of the free surfaces is therefore crucial when performing simulations. Today, there is a lack in the possibility to model such phenomenon with traditional methods. Hence, this work focuses on a parameter study for one alternative simulation tool available, namely the meshfree, Lagrangian particle method Smoothed Particle Hydrodynamics (SPH). The parameter study includes the choice of equation-of-state (EOS), the artificial viscosity constants, using a dynamic versus a static smoothing length, SPH particle spatial resolution and the finite element method (FEM) mesh scaling of the boundaries. The two dimensional SPHERIC Benchmark test case of dam break evolution over a wet bed was used for comparison and validation. The numerical results generally showed a tendency of the wave front to be ahead of the experimental results, i.e. to have a greater wave front velocity. The choice of EOS, FEM mesh scaling as well as using a dynamic or a static smoothing length showed little or no significant effect on the outcome, though the SPH particle resolution and the choice of artificial viscosity constants had a major impact. A high particle resolution increased the number of flow features resolved for both choices of artificial viscosity constants, but at the expense of increasing the mean error. Furthermore, setting the artificial viscosity constants equal to unity for the coarser cases resulted in a highly viscous and unphysical solution, and thus the relation between the artificial viscosity constants and the particle resolution and its impact on the behavior of the fluid needed to be further investigated.

Axial 3D effect on modeling a heterogeneous core

To assess the need of next generation method (NGM) for analyzing heterogeneous cores, a mini-core with 6×6 boiling water reactor (BWR) bundles is proposed as a benchmark problem. It is found that the traditional method based on reflective single bundle homogenization leads to very large errors even for a sliced 2D core analysis. For the 3D case there is very strong axial interface effect on fine mesh scale that has nothing to do with axial homogenization and cannot be captured by the traditional coarse mesh nodal method with radial pin power reconstruction. A single bundle 3D homogenization and pin power reconstruction model is proposed to couple with coarse mesh nodal method such that the detailed 3D effect of the reference solution can be reproduced accurately.

Development of CAD-to-CAE Model Preparation Technology

This paper explains and demonstrates how to reduce time for preparation of 3-dimensional (3D) geometrical Computer-Aided-Engineering (CAE) model from 3D Computer-Aided-Design (CAD) data. In generally, CAE model preparation is labor intensive and takes long time. Main part of preparation work is simplification of 3D-CAD data to decrease mesh scale and without impacting the solution accuracy. The purpose of this study is to create automatic CAE model preparation technology for reduction of preparation time. In this study, automatic model preparation method is developed by using of geometrical and topological information of 3D-CAD data. Benchmark test is performed to proof the efficiency of the method.

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.

Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy

Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order \(k+\frac{1}{2}\) to order 2k+1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272–289, 2007; Mirzaee et al. in SIAM J. Numer. Anal. 49:1899–1920, 2011). Additionally, it improves the weak continuity in the discontinuous Galerkin method to k−1 continuity. Typically this improvement has a positive impact on the error quantity in the sense that it also reduces the absolute errors. However, not enough emphasis has been placed on the difference between superconvergent accuracy and improved errors. This distinction is particularly important when it comes to understanding the interplay introduced through meshing, between geometry and filtering. The underlying mesh over which the DG solution is built is important because the tool used in SIAC filtering—convolution—is scaled by the geometric mesh size. This heavily contributes to the effectiveness of the post-processor. In this paper, we present a study of this mesh scaling and how it factors into the theoretical errors. To accomplish the large volume of post-processing necessary for this study, commodity streaming multiprocessors were used; we demonstrate for structured meshes up to a 50× speed up in the computational time over traditional CPU implementations of the SIAC filter.

Experimental and numerical study of oblique impact on woven composite sandwich structure: Influence of the firing axis orientation

During flight, aircrafts can be submitted to complex loadings. The reliability of their structure is an essential aspect in ensuring passenger safety. In the specific case of helicopters, blades are subjected to impact loading. The following work will focus on the experimental and numerical study of an oblique impact on the skin of the blade. It is equivalent in a first approach to an impact on a sandwich panel comprising a foam core and a thin woven composite skin. This study aims to identify the mechanisms of damage to the skin for different orientations of the firing axis, and to develop a representative model of the damage kinetics adapted to the modeling of the complete structure. Thus, an F.E. semi-continuous explicit model has been developed. It relies on the development of a specific damageable element at the woven mesh scale. Numerical results obtained are accurate, allowing the identification of the damage mechanism of the woven skin for different firing orientations.

Dimension splitting algorithm for a three-dimensional elliptic equation

This paper presents a finite-element dimension splitting algorithm (DSA) for a three-dimensional (3D) elliptic equation in a cubic domain. The main idea of DSA is that a 3D elliptic equation can be transformed into a series of two-dimensional (2D) elliptic equations in the X–Y plane along the Z-direction. The convergence speed of the DSA for a 3D elliptic equation depends mainly on the mesh scale of the Z-direction. P 2 finite-element discretization in the Z-direction for DSA is adopted to accelerate the convergence speed of DSA. The error estimates are given for DSA applying P 1 or P 2 finite-element discretization in the Z-direction. Finally, some numerical examples are presented. We apply the parallel solving technology to our numerical examples and obtain good parallel efficiency. These numerical experiments test and verify theoretical results.

Numerical Simulation of Fluctuating Propeller Forces and Comparison with Experimental Data

Unsteady CFD method based on realizable k-ε model is used for predicting unsteady forces of propeller working in non-uniform wake. First, CFD computations with different mesh scales were conducted at the propeller design condition, the results show that mesh refinement changed the results little. Then unsteady CFD simulation with different time step intervals was conducted for determining suitable time step interval, the results show that it is suitable for propeller rotating 3° per step. Based on the chosen mesh and time step interval, unsteady CFD simulation of propeller P4118 was conducted in 3-cycle and 4-cycle inflow, the unsteady thrust, torque and horizontal force agree well with experimental data, the results show that CFD method has good accuracy in predicting unsteady propeller forces.

Diesel engine emissions and combustion predictions using advanced mixing models applicable to fuel sprays

An advanced mixing model was applied to study engine emissions and combustion with different injection strategies ranging from multiple injections, early injection and grouped-hole nozzle injection in light and heavy duty diesel engines. The model was implemented in the KIVA-CHEMKIN engine combustion code and simulations were conducted at different mesh resolutions. The model was compared with the standard KIVA spray model that uses the Lagrangian-Drop and Eulerian-Fluid (LDEF) approach, and a Gas Jet spray model that improves predictions of liquid sprays. A Vapor Particle Method (VPM) is introduced that accounts for sub-grid scale mixing of fuel vapor and more accurately and predicts the mixing of fuel-vapor over a range of mesh resolutions. The fuel vapor is transported as particles until a certain distance from nozzle is reached where the local jet half-width is adequately resolved by the local mesh scale. Within this distance the vapor particle is transported while releasing fuel vapor locally, as determined by a weighting factor. The VPM model more accurately predicts fuel-vapor penetrations for early cycle injections and flame lift-off lengths for late cycle injections. Engine combustion computations show that as compared to the standard KIVA and Gas Jet spray models, the VPM spray model improves predictions of in-cylinder pressure, heat released rate and engine emissions of NOx, CO and soot with coarse mesh resolutions. The VPM spray model is thus a good tool for efficiently investigating diesel engine combustion with practical mesh resolutions, thereby saving computer time.

Connectivity‐consistent mapping method for 2‐D discrete fracture networks

We present a new flow computation method in 2‐D discrete fracture networks (DFN) intermediary between the classical DFN flow simulation method and the projection onto continuous grids. The method divides the simulation complexity by solving for flows successively at a local mesh scale and at the global domain scale. At the local mesh scale, flows are determined by classical DFN flow simulations and approximated by an equivalent hydraulic matrix (EHM) relating heads and flow rates discretized on the mesh borders. Assembling the equivalent hydraulic matrices provides for a domain‐scale discretization of the flow equation. The equivalent hydraulic matrices transfer the connectivity and flow structure complexities from the local mesh scale to the domain scale. Compared to existing geometrical mapping or equivalent tensor methods, the EHM method broadens the simulation range of flow to all types of 2‐D fracture networks both below and above the representative elementary volume (REV). Additional computation linked to the derivation of the local mesh‐scale equivalent hydraulic matrices increases the accuracy and reliability of the method. Compared to DFN methods, the EHM method first provides a simpler domain‐scale alternative permeability model. Second, it enhances the simulation capacities to larger fracture networks where flow discretization on the DFN structure yields system sizes too large to be solved using the most advanced multigrid and multifrontal methods. We show that the EHM method continuously moves from the DFN method to the tensor representation as a function of the local mesh‐scale discretization. The balance between accuracy and model simplification can be optimally controlled by adjusting the domain‐scale and local mesh‐scale discretizations.

Assessment of the methane mitigation potentials of alternative water regimes in rice fields using a process‐based biogeochemistry model

AbstractRice production is a substantial source of atmospheric CH4, which is second only to CO2 as a contributor to global warming. Since CH4 is produced in anaerobic soil environments, water management is expected to be a practical measure to mitigate CH4 emissions. In this study, we used a process‐based biogeochemistry model (DNDC‐Rice) to assess the CH4 mitigation potentials of alternative water regimes (AWR) for rice fields at a regional scale. Before regional application, we tested DNDC‐Rice using site‐scale data from three rice fields in Japan with different water regimes. The observed CH4 emissions were reduced by drainage of the fields, but were enhanced by organic amendments. DNDC‐Rice gave acceptable predictions of variation in daily CH4 fluxes and seasonal CH4 emissions due to changes in the water regime. For regional application, we constructed a GIS database at a 1 × 1 km mesh scale that contained data on rice field area, soil properties, daily weather, and farming management of each cell in the mesh, covering 3.2% of the rice fields in Japan's Hokkaido region. We ran DNDC‐Rice to simulate CH4 emissions under five simulated water regimes: the conventional water regime and four AWR scenarios with gradually increasing drainage. We found that AWR can reduce CH4 emission by up to 41% compared with the emission under conventional water regime. Including the changes in CO2 and nitrous oxide emissions, potential mitigation of greenhouse gas (GHG) was 2.6 Mg CO2 Eq. ha−1 yr−1. If this estimate is expanded to Japan's total rice fields, expected GHG mitigation is 4.3 Tg CO2 Eq. yr−1, which accounts for 0.32% of total GHG emissions from Japan. For a reliable national‐scale assessment, however, databases on soil, weather, and farming management must be constructed at a national scale, as these factors are widely variable between regions in Japan.

Pseudo-transient continuation-based variable relaxation solver in nonlinear magnetohydrodynamic simulations

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first- and/or second-order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray X1E. Two schemes are derived in this work, first- and second-order variable relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; next the system is carefully initialized by the solution with linear conductivity; third, time step and relaxation factor are vertex-based varied and optimized at each time step; finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

A domain decomposition methodology for pin by pin coupled neutronic and thermal–hydraulic analyses in COBAYA3

Nowadays, coupled 3D neutron-kinetics and thermal–hydraulic core calculations are performed by applying a radial average channel approach using a meshing of one quarter of assembly in the best case. This approach does not take into account the subchannels effects due to the averaging of the physical fields and the loose of heterogeneity in the thermal–hydraulic modelization. Therefore the models do not have enough resolution to predict those subchannels effects which are important for the fuel design safety margins, because it is in the local scale, where we can search the hottest pellet or the maximum heat flux. The aim of this paper is to present a domain decomposition methodology as our choice to asses this multi-scale issue in order to correct the results at the core scale with the ones from the subchannel scale. The UPM advanced multi-scale neutron-kinetics and thermal–hydraulics methodologies being implemented in COBAYA3 include domain decomposition by alternate core dissections for the local 3D fine-mesh scale problems (pin cells/subchannels) and an analytical nodal diffusion solver for the coarse mesh scale coupled with the thermal–hydraulic using a modelization of one channel per assembly or per quarter of assembly. The multi-scale domain decomposition is optimal for the thermal–hydraulic calculations, where the neutronic nodes (assemblies or quarters) can be mapped one-to-one to average channels and fuel rods and the pin cells to the detailed fuel pins and subchannels. For both levels we use the same channel code and, in order to facilitate the multi-scale mesh definition for the TH modules, the development of an input pre-processor has been a relevant part of this work.

Mesh watermarking based projection onto two convex sets

This paper proposes 3D-mesh watermarking based on projection onto convex sets (POCS). As such, a 3D-mesh model is iteratively projected onto two constraint convex sets until the convergence condition is satisfied. The sets consist of a robustness set and invisibility set designed to embed the watermark. The watermark can be extracted without the original mesh model using the decision values and index that the watermark was embedded with. Experimental results verify that the watermarked mesh model has both robustness against mesh simplification, cropping, scaling, rotation, translation, and vertex randomization and invisibility.