Discontinuous Fields Research Articles

A consistent diffuse-interface model for two-phase flow problems with rapid evaporation

We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several orders of magnitude, leading to high velocity and pressure jumps across the liquid–vapor interface, along with dynamically changing interface topologies. To this end, we integrate an incompressible Navier–Stokes solver combined with a conservative level-set formulation and a regularized, i.e., diffuse, representation of discontinuities into a matrix-free adaptive finite element framework. The achievements are three-fold: First, we propose mathematically consistent definitions for the level-set transport velocity in the diffuse interface region by extrapolating the velocity from the liquid or gas phase. They exhibit superior prediction accuracy for the evaporated mass and the resulting interface dynamics compared to a local velocity evaluation, especially for strongly curved interfaces.Second, we show that accurate prediction of the evaporation-induced pressure jump requires a consistent, namely a reciprocal, density interpolation across the interface, which satisfies local mass conservation. Third, the combination of diffuse interface models for evaporation with standard Stokes-type constitutive relations for viscous flows leads to significant pressure artifacts in the diffuse interface region. To mitigate these, we propose to introduce a correction term for such constitutive model types. Through selected analytical and numerical examples, the aforementioned properties are validated. The presented model promises new insights in simulation-based prediction of melt–vapor interactions in thermal multiphase flows such as in laser-based powder bed fusion of metals.

The Development of Tourism Areas in Abang Temple Yogyakarta, Using Engineering Geological Capability

Temples are interesting objects used for the exploration, exploitation, and development of tourist areas. However, these cultural sites and the surrounding environment need to be adequately preserved to prevent disasters. One of the interesting aspects of temples needed to be developed as tourist areas is its engineering geological capability. Therefore, this study aims to determine the engineering geological capability of Abang Temple located in the village of Jogotirto, Berbah, Sleman, Yogyakarta, Indonesia. This Buddhist heritage temple was built on an isolated hill with the constituent materials of red bricks, tuff, and andesite that have experienced weathering over the decades. The temple is geographically located in an interesting natural nuance, thereby making it a dilemma for developing tourist areas. This research was carried out by mapping and measuring field data on several influential aspects, including the carrying capacity of rocks and soil, slope, the potential for geological disasters, the depth of groundwater level, the ease of excavation, the land use, the rock weathering level, and the discontinuity field density. The results shows that there are three zones of engineering geological capability for developing temples into tourist areas, namely high, medium, and low capabilities.

The magnetic gradient tensor of a right circular cylinder: theoretical considerations in the determination of magnetisation direction

This paper investigates the use of the magnetic gradient tensor and its eigenvectors to derive expressions for estimating the direction of magnetisation of a uniformly magnetised right circular vertical cylinder. Expressions for the gradient tensor, the eigenvalues and eigenvectors, the normalised source strength (NSS), and the direction of magnetisation on the axis of a vertical cylinder are shown to be identical in form to those previously derived for a magnetised sphere or dipole. However, the off-axis gradient tensor field of a vertical cylinder is significantly different to that of a magnetic sphere or dipole particularly at low observation heights. These differences lessen with increasing observation height and in more compact pipes. The normalised source strength displays a directional asymmetry in the eigenvector field of the gradient tensor above a pipe which is related to the direction of magnetisation. This azimuthal asymmetry in the NSS results exclusively from the horizontal components of magnetisation, which are perpendicular to the longitudinal face of the vertical cylinder. In contrast, the vertical component of magnetisation is normal to the circular planar face and produces radial symmetry in the NSS. Additionally, the paper details some unusual properties of the NSS which are attributable to non-dipole field components in the gradient tensor field which cause pairs of eigenvectors to interchange directions when ordered by their eigenvalues, as is done when calculating the NSS. This results in spatial discontinuities in the eigenvector fields arising from crossovers in the ordered eigenvalue surfaces which vary with both magnetisation direction and observation height. This phenomenon is not present in a dipole field and thus provides direct evidence of non-dipole field components. Understanding this complexity in the eigenvector field is essential to designing methodologies which can successfully estimate the direction of magnetisation over a uniformly magnetised cylinder. One proposed method based on the peak NSS, uses airborne gradient tensor data to accurately estimate magnetisation direction over a reversely magnetised pipe-like body in the Diavik diamond field of north-western Canada. The results are verified using a full tensor inversion.

MorphFlow: Estimating Motion in In-Situ Tests of Concrete

Abstract Background In situ Computed Tomography is a valuable tool to investigate failure mechanics of materials in 3D. For brittle materials with sudden fracture like concrete however, state-of-the-art methods such as Digital Volume Correlation fail to produce displacement fields that display the discontinuous behavior of load induced cracking correctly. Objective The main objective is to develop an algorithm that calculates displacement fields for large-scale in situ experiments on concrete. Methods The algorithm presented is based on a 3D Optical Flow method solved by a primal-dual procedure and equipped with a coarse-to-fine scheme based on morphological wavelets. The algorithm is publicly available. Our evaluation focuses on the beneficial use of morphological wavelets over classical ones, and on the ability to produce reliable results with limited data. Applying the primal-dual scheme to in situ tests and using morphological wavelets are novel contributions. Results The results show that our algorithm cannot only cope with large volume images, but also produces discontinuous displacement fields that yield high strain in fractured regions. It does not only perform better than state-of-the-art methods, but also achieves sufficient results on reduced data. The morphological wavelets play a key role in this finding - they even allow to deduce cracks of widths less than a voxel. Conclusion Displacement calculation for in situ tests of brittle materials requires voxel-accurate displacement fields that allow for discontinuities. The presented algorithm fulfills these requirements and therefore is a powerful tool for future understanding of failure mechanics in concrete.

Simplified discontinuous field model for RC beams with a medium shear span ratio: Experimental study and shear strength formula

It is generally believed that the shear span ratio is one of critical factors governing the shear failure of reinforced concrete beams. For a certain shear span scenario, the shear transfer mechanism is often attributed to one of the two typical categories: ‘beam-action’ for slender beams with a large shear span ratio, and ‘arch-action’ in deep beams with a small shear span ratio. However, in the medium shear span ratio range, neither the beam action nor the arch action dominates. In this study, an alternative model based on the notion of discontinuous fields is established under the framework of limit analysis. A shear strength formula for medium shear spans is derived subsequently by solving a combined action of the smeared-arch subfield and the vertical stirrups linking the fan subfield. After that, the least shear strength is obtained via the kinematic analysis of these discontinuous fields. To examine the proposed model, an experimental study is conducted through two T-beam specimens with artificially preset cracks and two benchmark specimens. In comparison with existing approaches and test results collected from this study and other twenty-two specimens in the literature, the proposed discontinues field model has a fairly good agreement in the shear strength predictions. A further discussion on the advantages and limitations of the simplified discontinuous field model also demonstrates that it provides a better transition of the shear strength verifications between slender beams and deep beams.

Three-dimensional compact multi-resolution weighted essentially non-oscillatory reconstruction under the Arbitrary Lagrange–Euler framework

A third-order compact multi-resolution weighted essentially non-oscillatory (CMR-WENO) reconstruction method for three-dimensional (3D) hybrid unstructured grids is developed using the Arbitrary Lagrange–Euler framework. The finite volume method is used to discretize the governing equations, and some turbulent and moving boundary problems are simulated. Only one compact center stencil comprising the neighboring cells of each control cell is required to construct the polynomials in the algorithm. As a result, the number of stencils and stencil cells is significantly reduced when compared with the traditional WENO scheme. This simplifies the code and improves the robustness of the algorithm. By ensuring the cell average and first-order derivatives are consistent with that in stencil cells an over-determined system of equations can be used to reconstruct the polynomials. This system can then be solved using the compact least squares method to avoid an ill-conditioned coefficient matrix. Furthermore, a coupled implicit iteration strategy is used to solve for the unknown coefficients, so no extra determination is required for the derivatives of each control cell. The final interpolation function for discontinuities in the flow field is obtained using CMR-WENO to nonlinearly combine polynomials of different orders, which further improves the stability of the algorithm. The CMR-WENO can be implemented on 3D hybrid unstructured grids and can be used to simulate complex problems such as those involving turbulence and moving boundaries. Finally, the algorithm presented here is verified to be third-order accurate and to exhibit good robustness when used on several representative numerical examples.

Reassembling the Field-based Applicability of the Lactate Threshold for Old Age.

This study aimed to investigate the applicability of the Lactate Threshold (LT) to predict maximal oxygen uptake (˙VO2max) and demarcate the boundary between the moderate- to heavy-intensity domain (HRm-h) in old age in comparison to the most utilized methods. A cross-sectional validation study was conducted. Participants aged 61 to 77 performed a familiarization procedure, an incremental maximal exercise treadmill test (CPX) for ˙VO2max determination, the Six-minute Walk Test (6MWT), and a discontinuous incremental field test for LT determination. Lower (P<0.01) internal effort was required for LT testing (76±8%HRmax) compared to 6MWT (92±9%HRmax). The application of the 6MWT reference equations overestimated ˙VO2max by 10-23%. LTs better estimated the ˙VO2max (r ≈0.90, SEE: ≈3.0] compared to the 6MWT (r=0.68, SEE=5.5). HRm-h determined by the CPX differed (20%; P=0.001) from that obtained by LT. HRm-h stratification indicated participants fall into the very light to the vigorous intensity domains. LT testing is more submaximal than the 6MWT, and is a valuable tool to estimate the ˙VO2max in older male adults. Implementation of LT testing in physical activity programs might help improving the quality of aerobic exercise training in older men.

Weyl Points on Nonorientable Manifolds.

Weyl fermions are hypothetical chiral particles that can also manifest as excitations near three-dimensional band crossing points in lattice systems. These quasiparticles are subject to the Nielsen-Ninomiya "no-go" theorem when placed on a lattice, requiring the total chirality across the Brillouin zone to vanish. This constraint results from the topology of the (orientable) manifold on which they exist. Here, we ask to what extent the concepts of topology and chirality of Weyl points remain well defined when the underlying manifold is nonorientable. We show that the usual notion of chirality becomes ambiguous in this setting, allowing for systems with a nonzero total chirality. This circumvention of the Nielsen-Ninomiya theorem stems from a generic discontinuity of the vector field whose zeros are Weyl points. Furthermore, we discover that Weyl points on nonorientable manifolds carry an additional Z_{2} topological invariant which satisfies a different no-go theorem. We implement such Weyl points by imposing a nonsymmorphic symmetry in the momentum space of lattice models. Finally, we experimentally realize all aspects of their phenomenology in a photonic platform with synthetic momenta. Our work highlights the subtle but crucial interplay between the topology of quasiparticles and of their underlying manifold.

Hybrid meshless-FEM method for 3-D magnetotelluric modelling using non-conformal discretization

SUMMARY We propose a novel method for 3-D magnetotelluric (MT) forward modelling based on hybrid meshless and finite-element (FE) methods. This method divides the earth model into a central computational region and an expansion one. For the central region, we adopt scatter points to discretize the model, which can flexibly and accurately characterize the complex structures without generating unstructured mesh. The meshless method using compact support radial basis function is applied to simulate this area's electromagnetic field. While in the expansion region, to avoid the heavy time consumption and numerical error of the meshless method caused by non-uniform nodes, we adopt a node-based finite-element method with regular hexahedral mesh for stability. Finally, the two discretized systems are coupled at the interface nodes according to the continuity conditions of vector and scalar potentials. Considering that the normal electric field is discontinuous at the interface with resistivity discontinuity, while the shape functions for the meshless method are continuous, we further adopt the visibility criterion in constructing the support region. Numerical experiments on typical models show that using the same degree of freedom, the hybrid meshless-finite element method (FEM) algorithm has higher accuracy than the node-based FEM and meshless method. In addition, the electric field discontinuity at interfaces is well preserved, which proves the effectiveness of the visibility criterion method. In general, compared to the conventional grid-based method, this new approach does not need the complex mesh generation for complex structures and can achieve high accuracy, thus it has the potential to become a powerful 3-D MT forward modelling technique.

Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems

AbstractImmersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a structured background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the structured background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed isogeometric method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchically refined B-splines (THB-splines) is used to both improve interface geometry representations and to resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for partial differential equations representing heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom when compared to classical boundary-fitted finite element methods.

Damage evolution of coal with a strong bursting liability and 3D measurement method for elastic deformation energy distribution

When coal with a strong bursting liability is disturbed by a load, catastrophic instability disasters and rockbursts can easily occur. Loaded coal with a strong bursting liability undergoes complex damage evolution and failure behavior due to the intricate interplay among loads, gangue, fractures, and the coal matrix. Intuitively quantifying and characterizing the complex discontinuous structural features, deformation fields, and energy fields within coal is the foundation for the scientific analysis and prevention of disaster mechanisms caused by rockbursts. Therefore, studying the distribution and evolutionary processes of deformation fields and energy fields caused by the evolution of discontinuous structures within coal is highly important for the prevention and control of coal mine rockburst disasters and the protection of coal mine safety during mining operations. In this study, a series of X-ray computed tomography (X-CT) tests were conducted on coal specimens with varying gangue contents under uniaxial compressive loading. The X-CT images clearly illustrated the internal damage evolution of coal with a strong bursting liability, revealing fracture propagation, shear bands, and localized failure under varying loading conditions. Image segmentation was employed to quantitatively analyze the development of damage in coal with a strong bursting liability, revealing the influence patterns of gangue content on the prepeak deformation localization and strength of coal. Additionally, using digital volume correlation, the 3D volumetric displacement and strain of loaded impact-prone coal were determined based on the changes in natural speckle images. The nonuniform distribution of strain was mainly caused by the nonuniform distribution of gangue and pore fractures at the microscopic scale, which explains the localized deformation in coal materials. Importantly, this study provides new full-field strain tensor data and a novel method for measuring the elastic deformation energy of the 3D deformation and cracking processes of loaded coal.

Quantification of Resection Margin following Sublobar Resection in Lung Cancer Patients through Pre- and Post-Operative CT Image Comparison: Utilizing a CT-Based 3D Reconstruction Algorithm.

Sublobar resection has emerged as a standard treatment option for early-stage peripheral non-small cell lung cancer. Achieving an adequate resection margin is crucial to prevent local tumor recurrence. However, gross measurement of the resection margin may lack accuracy due to the elasticity of lung tissue and interobserver variability. Therefore, this study aimed to develop an objective measurement method, the CT-based 3D reconstruction algorithm, to quantify the resection margin following sublobar resection in lung cancer patients through pre- and post-operative CT image comparison. An automated subvascular matching technique was first developed to ensure accuracy and reproducibility in the matching process. Following the extraction of matched feature points, another key technique involves calculating the displacement field within the image. This is particularly important for mapping discontinuous deformation fields around the surgical resection area. A transformation based on thin-plate spline is used for medical image registration. Upon completing the final step of image registration, the distance at the resection margin was measured. After developing the CT-based 3D reconstruction algorithm, we included 12 cases for resection margin distance measurement, comprising 4 right middle lobectomies, 6 segmentectomies, and 2 wedge resections. The outcomes obtained with our method revealed that the target registration error for all cases was less than 2.5 mm. Our method demonstrated the feasibility of measuring the resection margin following sublobar resection in lung cancer patients through pre- and post-operative CT image comparison. Further validation with a multicenter, large cohort, and analysis of clinical outcome correlation is necessary in future studies.

A physics-constrained and data-driven method for modeling supersonic flow

A fast solution of supersonic flow is one of the crucial challenges in engineering applications of supersonic flight. This article introduces a deep learning framework, the supersonic physics-constrained network (SPC), for the rapid solution of unsteady supersonic flow problems. SPC integrates deep convolutional neural networks with physics-constrained methods based on the Euler equation to derive a new loss function that can accurately calculate the flow fields by considering the spatial and temporal characteristics of the flow fields at the previous moment. Compared to purely data-driven methods, SPC significantly reduces the dependency on training data volume by incorporating physical constraints. Additionally, the training process of SPC is more stable than that of data-driven methods. Taking the classic supersonic forward step flow as an example, SPC can accurately calculate strong discontinuities in the flow fields, while reducing the data volume by approximately 60%. In the generalization test experiment for forward step flow and compression ramp flow, SPC also demonstrates good predictive accuracy and generalization capability under different geometric configurations and inflow conditions.

Изотермическое прессование в конической матрице релаксирующего материала

The relations for calculating the deformation mode and force conditions of isothermal extrusion of blanks made of high-strength metallic alloys are proposed. Under isothermal deformation, the material is hardened and softened, which is associated with the manifestation of the viscous properties of the material (creep). In this regard, the state of viscoplasticity is taken on. The deformation state is accompanied by stress relaxation, which is greater the lower the speed (longer duration) of the operation. Based on the mechanics of deformation, the dependence of moulding conditions (deformation, force, damage to the work material) is expressed by analytical relations. The power balance of activity of forces results in a pressure estimation for isothermal exposure. In this case, a discontinuous field of path velocities is used, which consists of a block of deformations and rigid blocks. The blocks are separated by slip surfaces. Deformations occur in the deformation block and on slip surfaces. Since pressing leads to the occurrence of micro-damages, the damage rate of the coating material was estimated. In this case, the criteria of fracture kinetics are used: energy and deformation equations. The damage rate of the material depends on the speed and degree of deformation, or solely on the degree of deformation. For a number of materials, reducing the speed helps to reduce damage and, consequently, the possibility of increasing the degree of shaping of the primary blank. The relations for stiffness analysis of the stress pattern are given, on which the damage also depends. Calculations of the pressure and damage of the material under compaction for blanks made of titanium and high-strength aluminum alloys have been performed. It is shown that at low operation speeds on the appropriate hydraulic forging equipment, the exposure pressure decreases significantly. The aluminum alloy damaging is also reduced, and for titanium it depends only on the degree of forming.

Joshi–Malafarina–Narayan singularity in weak magnetic field

The importance and significance of magnetic fields in the astrophysical scenario is well known. Many domains of astrophysical black hole physics such as polarized shadow image, high energy emitting processes and jet formation are dependent on the behavior of the magnetic fields in the vicinity of the compact objects. In light of this, we determine the master equation and master differential equation that determine the spatial behavior of the magnetic field inside a matter distribution or vacuum region, of general spherically symmetric metric, which is immersed in a test magnetic field. We also investigate here the case of JMN-1 singularity immersed in a uniform weak magnetic field and determine the behavior of magnetic fields by defining electromagnetic four potential vector. We find that the tangential component of the magnetic field is discontinuous at the matching surface of the JMN-1 singularity with the external Schwarzschild metric, resulting in surface currents. We define the covariant expression of surface current density in this scenario. We also analyze the behavior of center-of-mass energy of two oppositely charged particles in the geometry of the magnetized JMN-1 singularity. We briefly discuss the possible scenarios which would possess a discontinuous magnetic field and implications of the same and future possibilities in the realm of astrophysics are indicated.

Orientation of IMF Discontinuity Normals Across the Solar Cycles

AbstractTransient events like hot flow anomalies and foreshock bubbles are common in the Earth's foreshock. These foreshock transients may play an important role in the solar wind‐magnetosphere interaction. They typically occur when backstreaming ions accumulate at the intersection of interplanetary magnetic field (IMF) discontinuities with the bow shock. Discontinuity orientations play a key role in determining when and where transients form in the foreshock and strike the magnetopause. They also play a role in determining the amplitude, and significance, of individual transients. We investigate properties of the IMF discontinuity normals across two solar cycles. We compare Advanced Composition Explorer (ACE) IMF discontinuity observations for 2001, 2002, 2012, and 2014 (solar maximum) and 2008, 2009, 2019, and 2020 (solar minimum). We employ both the Minimum variance analysis (MVA) and Cross‐product methods to determine phase front normals. Most discontinuity normals point earthward and dawnward at longitudes ranging from 180° to 250°. A greater range of normal can be seen during solar minimum than during solar maximum. Normals lie further from the Sun‐Earth line when solar wind densities are low and velocities are high. This provides a natural explanation for the observed tendency of transients to occur for low solar wind densities and high velocities in terms of longer discontinuity interaction times with the bow shock.

Voltage-tunable graphene-InP schottky photodetector with enhanced responsivity using plasmonic waveguide integration

In this work, we propose and theoretically investigate a novel side-illuminated graphene Schottky photodetector (SIGS-PD) integrated on an InP waveguide platform suitable for the telecommunication wavelength of 1.55 μm. Bilayer graphene is positioned to absorb the transverse magnetic (TM) mode, with an InP substrate forming a Schottky junction to enable electrical connectivity and carrier separation. Through electrostatic gating, the graphene Fermi level is actively tuned to reach an epsilon-near-zero condition of 0.51 eV, transitioning the optical properties from dielectric to metallic. This supports reconfigurable plasmonic modes confined within the subwavelength graphene layer, interacting strongly with the TM optical mode. Responsivity of TM mode is enhanced 10 × TE mode reaching 1.24 A W−1 at the epsilon-near-zero point for the wavelength of 1.55 μm due to discontinuity and localization of the perpendicular electric field. The maximum responsivity is achieved at reverse bias of 4.5 V for device lengths under 4 μm. Dark current is suppressed to 10−15 A by the rectifying Schottky junction. An internal specific detectivity of 9.6 × 1012 Jones is predicted along with >25 GHz bandwidth, exploiting combined benefits of plasmonic enhancement and electrical transport control in the hybrid graphene-InP platform. The voltage-tunability of the graphene optical properties provides a pathway to dynamically optimize device performance. This work demonstrates a route towards high-responsivity and high-speed graphene photodetectors seamlessly integrated with photonic integrated circuits.

Non-break modeling and numerical simulation for non-intact rock failure process

Simulation of the failure process of non-intact rock containing initial cracks, voids, and other discontinuities is a research hotspot in rock mechanics and geotechnical engineering. The damage smear method has attracted wide attention due to its ability to realistically depict the complete failure processes of rock from the microscopic to the macroscopic scale. However, when portraying pre-existed discontinuities, the damage smear method suffers from major difficulties such as mesh dependency and stress singularity. To overcome the limitations of current methodology, this paper proposes a novel non-break modeling strategy inspired by the extended finite element method for dealing with embedded discontinuities, in which the discontinuity of the physical fields across crack faces or the void boundary, as well as the stress singularity at the crack tip, can be characterized by introducing appropriate enrichment functions, and the penalty method is used to impose frictional contact constraints. Applications of the combined method of the improved modeling strategy and damage smear analysis to laboratory-scale and engineering-scale numerical examples show a satisfactory approximation with the analytical solution or experimental observations, indicating that the current modeling strategy can further improve computational accuracy while retaining the advantages of the damage smear method.

Spiking NeRF: Representing the Real-World Geometry by a Discontinuous Representation

A crucial reason for the success of existing NeRF-based methods is to build a neural density field for the geometry representation via multiple perceptron layers (MLPs). MLPs are continuous functions, however, real geometry or density field is frequently discontinuous at the interface between the air and the surface. Such a contrary brings the problem of unfaithful geometry representation. To this end, this paper proposes spiking NeRF, which leverages spiking neurons and a hybrid Artificial Neural Network (ANN)-Spiking Neural Network (SNN) framework to build a discontinuous density field for faithful geometry representation. Specifically, we first demonstrate the reason why continuous density fields will bring inaccuracy. Then, we propose to use the spiking neurons to build a discontinuous density field. We conduct a comprehensive analysis for the problem of existing spiking neuron models and then provide the numerical relationship between the parameter of the spiking neuron and the theoretical accuracy of geometry. Based on this, we propose a bounded spiking neuron to build the discontinuous density field. Our method achieves SOTA performance. The source code and the supplementary material are available at https://github.com/liaozhanfeng/Spiking-NeRF.

Microstructural smoothed particle hydrodynamics model and simulations of discontinuous shear-thickening fluids

Despite the recent interest in the discontinuous shear-thickening (DST) behavior, few computational works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation of a microstructural DST model in smoothed particle hydrodynamic (SPH) simulation. The scalar model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios of local to non-local microstructural effects were probed: zero, moderate, and strong non-locality. Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–Cates (WC) model, with the moderate case exhibiting banding patterns. We demonstrate that a local model is prone to a stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC model. The mechanism of stress splitting has been explored and contextualized by the interaction of local microstructure evolution and the stress-control scheme. Analytic solutions for a body-force-driven DST channel flow have been derived and used to validate the SPH simulations with excellent agreement in velocity profiles. Simulations carried out at increasing driving forces exhibited a decrease in flow. We showed that even the simple scalar model can capture some of the key properties of DST materials, laying the foundation for further SPH study of instabilities and pattern formation.