3D Numerical Simulations Research Articles

Investigating Subsurface Properties of the Shallow Lunar Crust Using Seismic Interferometry on Synthetic and Recorded Data

AbstractIn the past few years, the remarkable progress of commercially operated spacecrafts, the success with reusable rocket engines, as well as the international competition to explore space, has led to a substantial acceleration of activities in the design and preparation of ambitious future lunar missions. In the search for ice and/or cavities imaging the shallow subsurface structure is of vital importance. Hereby, previous studies have shown that seismic interferometry is a promising method to investigate the subsurface properties from passive lunar data. In this study, we want to evaluate the potential of this method further by examining the required duration of seismic measurements and the influence of scattering on the Green's function retrieval. Therefore, we applied seismic interferometry to both measured Apollo 17 data and synthetic data. Our findings indicate that, under optimal conditions, a few hours of data are sufficient when using the method of time‐scaled phase‐weighted stack (ts‐PWS). However, this strongly depends on the inter‐station distance, the orientation toward the principal noise sources, and the timing of the measurement during the lunar cycle. Additionally, we were able to reproduce the measured data using numerical simulations in 2D. The synthetic results show that scattering effects clearly influence the Green's function extraction, especially for larger station distances.

Mathematical modeling of the chemotaxis-biodenitrification process

In this paper, we develop and study a new mathematical model to describe the good functioning of the biodenitrification process, combining both the biological and the mechanical aspects, and taking into account the chemotaxis-phenomenon. The model is governed by a non-linear reaction-diffusion-advection system for the bacterial activity and the Darcy flow for the porous medium. We prove the existence and uniqueness of the solution and we carry out the numerical approximation of the model within a variational framework. We propose a full discrete system based on a finite element method and we perform numerical simulations both in 2D and 3D.

The 34th German CFD network of competence meeting: numerical 3D simulation of reactor primary cooling circuit and containment flows

Abstract The 34th German CFD Network of Competence Meeting was held in March 2023 at the Gesellschaft für Anlagen-und Reaktorsicherheit (GRS) gGmbH in Garching, Germany. Twenty-one scientific presentations, distributed in the two sessions “Simulation of Reactor Cooling Circuit Flows” and “Simulation of Reactor Containment Flows” were presented. This paper gives a short summary of the different contributions.

Thermal network model for anisotropic heat transfer in 3D printed complex geometry structures

The sustainability of 3D printed buildings has drawn increasing attention in research. As a foundation for assessing energy efficiency and sustainability, it is crucial to consider the thermal performance of 3D printed walls during the structural design phase. 3D printed walls exhibit anisotropic thermophysical properties and complex heat transfer processes. However, there is a lack of studies accounting for these aspects. This work proposes a thermal network model suitable for objects with changing directions of principal thermal conductivities. The key is to store information on sizes, directions and properties. Analytical solution verification and experimental verification under two-dimensional conditions agree well with the actual results. The numerical simulation of the anisotropic 3D printed wall with complex geometry shows that the reinforced structures and the cavities cause alternating surface temperature distributions, with an average temperature difference of about 0.75 °C. Due to the barrier effect of the inclined printed structure, the triangular cavities show higher temperatures than the square cavities. The proposed model is significant for characterizing the relationship between structure and thermal performance and can be used to optimise the thermal design of 3D printed walls.

Double field of view digital sideband holography as an optimized method to measure velocity fields in a large fluid volume

Digital in-line holography is a technique that allows the measurement of the three velocity components of a three dimensional fluid flow. The application of digital in-line holography in fluid velocimetry is mainly limited by three factors: the sensor size that limits the transversal area that can be recorded, the low optical aperture that reduces the spatial resolution along the optical axis and introduces aliasing, and the noise coming from the twin image that hinders the particle position and velocity measurements. These factors do not affect in the same way when characterizing the movement of the fluid, and require different solutions.In this work we are going to show how to overcome those limitations. We applied digital sideband holography for the measurement of the particle position and velocity in a fluid volume with a cross-section twice the area allowed by the camera sensor, with magnification M = 1, and a very large the dimension along the optical axis. Digital sideband holography configuration, that keeps the simplicity of the classical in-line holographic set-up, consists of a camera, a lens and a frequency filter. This frequency filter is the key element that allows us to measure in such a large volume while maintaining spatial resolution, as well as accuracy: not only removes the twin image but also prevents the recording of unwanted frequencies that causes aliasing. We have found that the Signal to Noise Ratio depends mainly on the noise introduced by the twin image, the aliasing and the particle concentration rather than on parameters such as field of view, depth of field or the intensity of the particles.This technique is applied for the quantitative characterization of the three-dimensional flow in a lid-driven squared-sectioned cuvette. The introduction of a prism in the optical set-up allowed us to double the field of view. This is achieved by illuminating two volumes of the cuvette (22 × 22 × 100 mm3, each) with the same beam that crosses the fluid twice before reaching the camera sensor. These two fluid volumes are analyzed independently while keeping the same spatial resolution in the axial component along the whole volume than the expected for a shorter one. The experimental 3D data show a very good agreement with numerical 3D simulation, which proves the very good performance of our method.

Distributed parameter identification for the Navier–Stokes equations for obstacle detection

We present a parameter identification problem for a scalar permeability field and the maximum velocity in an inflow, following a reference profile. We utilize a modified version of the Navier–Stokes equations, incorporating a permeability term described by the Brinkman’s Law into the momentum equation. This modification takes into account the presence of obstacles on some parts of the boundary. For the outflow, we implement a directional do-nothing condition as a means of stabilizing the backflow. This work extends our previous research published in (Aguayo et al 2021 Inverse Problems 37 025010), where we considered a similar inverse problem for a linear Oseen model with do-nothing boundary conditions on the outlet and numerical simulations in 2D. Here we consider the more realistic case of Navier–Stokes equations with a backflow correction on the outflow and 3D simulations of the identification of a more realistic tricuspid cardiac valve. From a reference velocity that could have some noise or be obtained in low resolution, we define a suitable quadratic cost functional with some regularization terms. Existence of minimizers and first and second order optimality conditions are derived through the differentiability of the solutions of the Navier–Stokes equations with respect to the permeability and maximum velocity in the inflow. Finally, we present some synthetic numerical test based of recovering a 2D and 3D shape of a cardiac valve from total and local velocity measurements, inspired from 2D and 3D MRI.

An Effective Model for the Simulation of Transpiration Cooling

Transpiration cooling is numerically investigated, where a cooling gas is injected through a carbon composite material into a hot gas channel. To account for microscale effects at the injection interface, an effective problem is derived. Here, effects induced by microscale structures on macroscale variables, e.g., cooling efficiency, are taken into account without resolving the microscale structures. For this purpose, effective boundary conditions at the interface between hot gas and porous medium flow are derived using an upscaling strategy. Numerical simulations in 2D with effective boundary conditions are compared to uniform and non-uniform injection. The computations confirm that the effective model provides a more efficient and accurate approximation of the cooling efficiency than the uniform injection.

Patterning of nonlocal transport models in biology: The impact of spatial dimension

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their awareness of other animals. Nonlocal integro-PDE models have been used to investigate contact attraction and repulsion in cell populations in 1D. In this paper, we generalise the analysis of pattern formation in such a model from 1D to higher spatial dimensions. Numerical simulations in 2D demonstrate complex behaviour in the model, including spatio-temporal patterns, multi-stability, and patterns with wavelength and shape that differ significantly depending on whether interactions are attractive or repulsive. Through linear stability analysis in N dimensions, we demonstrate how, unlike in local Turing reaction–diffusion models, the capacity for pattern formation fundamentally changes with dimensionality for this nonlocal model. Most notably, pattern formation is possible only in higher than one spatial dimension for both the single species system with repulsive interactions, and the two species system with ‘run-and-chase’ interactions. The latter case may be relevant to zebrafish stripe formation, which has been shown to be driven by run-and-chase dynamics between melanophore and xanthophore pigment cells.

Surface roughness influence on photonic nanojet parameters of dielectric microspheres

All naturally found and technologically fabricated solid microparticles possess surface roughness. Upon optical wave scattering from such particles, in addition to its geometric shape, the surface relief becomes an important morphological factor determining the optical properties of the scatterer. We present results of the numerical 3D-simulations of focusing an optical wave with a dielectric microsphere with randomly distributed surface roughness. We address different cases of azimuthally symmetric and asymmetric distortions of the particle surface. We show that the key parameters of the near-field focal region (intensity, longitudinal and transverse dimensions) referred to as a photonic nanojet (PNJ) are sensitive to changes in the microsphere surface texture. Two important PNJ parameters, the peak intensity and the longitudinal length, are subject to more prominent changes. The influence of the optical contrast (relative refractive index) of the microsphere on PNJ parameters is investigated in detail. The possibility of reducing the influence of surface roughness on the near-field focusing strength by microsphere watering (water-uptake) is demonstrated.

Numerical Analysis of a Structure-Preserving Space-Discretization for an Anisotropic and Heterogeneous Boundary Controlled $N$-Dimensional Wave Equation As a Port-Hamiltonian System

The anisotropic and heterogeneous N-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. The recent structure-preserving Partitioned Finite Element Method is applied, leading directly to a finite-dimensional port-Hamiltonian system, and its numerical analysis is done in a general framework, under usual assumptions for finite element. Compatibility conditions are then exhibited to reach the best trade off between the convergence rate and the number of degrees of freedom for both the state error and the Hamiltonian error. Numerical simulations in 2D are performed to illustrate the optimality of the main theorems among several choices of classical finite element families.

Mechanical properties and numerical simulation of FDM 3D printed PETG/carbon composite unit structures

Carbon fibers (CFs) were used as reinforcement in developing a polyethylene terephthalate glycol (PETG)-based polymer composite using the fused deposition modeling (FDM) 3D printing technique. The influence of CF and process factors (infill percentage, layer thickness, infill pattern) were studied by measuring the prepared polymer composite's tensile, flexural, and compressive properties. The innovative work that was carried out for this study and the tests that were performed revealed that it is difficult to predict the position of the specimen break area before a test. The PETG-reinforced polymer only showed enhanced flexural and tensile strength at a layer thickness of 0.25 mm and a maximum infill percentage of 20% for a solid structural design. Compressive strength improved in reinforced PETG hexagonal and circle structures. The confirmation of the numerical modeling applied to determine the mechanical properties of PETG for FDM additive manufacturing is one of the goals suggested in this research, along with a comparison of experimental and computational data. Scanning electron microscopy examination of the fractured sample surfaces revealed various fracture mechanisms and morphologies for the materials tested. The research found that the 3D-printed composite could further expand the application of PETG as an engineering material.

The 33rd German CFD Network of Competence Meeting: 20 years of advances in the numerical 3D simulation of reactor relevant flows

Abstract The 33rd German CFD Network of Competence Meeting was held in March 2022 at the Gesellschaft für Anlagen-und Reaktorsicherheit (GRS) gGmbH in Garching, Germany. In 2022 the meeting celebrates its 20th anniversary with 17 scientific presentations, distributed in two main sessions: “Simulation of Reactor Cooling Circuit Flows” and “Simulation of Reactor Containment Flows”. This paper gives an overview of the different contributions, presented at this anniversary meeting, and also provides information on the background and the objectives of the German CFD Network of Competence.

Numerical 3D Simulation of Heat Transfer during Friction Stir Welding

Numerical 3D Simulation of Heat Transfer during Friction Stir Welding

Numerical approximation of SAV finite difference method for the Allen–Cahn equation

In this paper, the second-order scalar auxiliary variable approach combined with finite difference method is employed for the Allen–Cahn equation that represents a phenomenological model for antiphase domain coarsening in a binary mixture. The second-order backward differentiation formula is used in time. The error estimation of the semi-discrete scheme is derived in the sense of [Formula: see text]-norm. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of the proposed scheme.

A second-order Strang splitting scheme with exponential integrating factor for the Allen–Cahn equation with logarithmic Flory–Huggins potential

In this paper, we mainly consider the numerical approximation for the Allen-Cahn(AC) equation with logarithmic Flory–Huggins potential. It is well-known that the logarithmic Flory–Huggins potential is more physically significant than the generally employed fourth-order polynomial potential in various phase-field models. Nevertheless, owing to the singularity of the logarithmic term and the strong nonlinearity of the energy potential function, it is extremely challenging to develop an effective and easy-to-implement numerical scheme that preserves the maximum principle and energy dissipation law. To overcome these difficulties, we construct a second-order Strang splitting scheme with exponential integrating factor. Firstly, base on the idea of dimensional splitting, a new time dependent function, which is called exponential integrating factor is introduced. Then we propose the Strang splitting approach which is aim to decompose the original equation into linear part and nonlinear part. In particular, the logarithmic term is treated by explicit 2-stage strong stability preserving Runge–Kutta(SSP-RK2) method. Furthermore, we rigorously demonstrate the maximum principle, energy stability and convergence in details for the proposed scheme. A variety of numerical simulations in 2D and 3D are presented to confirm the validity of the proposed method.

Design and mechanical evaluation of a large cranial implant and fixation parts

Cranial implants are designed based on patient Digital Imaging and Communications in Medicine data. An asymmetric approach is usually employed to design cranial implants, and fixation plates are used to fix the implant. In this study, the use of numerical simulation of 3D (3 Dimension) cranial implants made from Polyether Ether Ketone was investigated. A skull defect reconstruction was conducted using Computer-Aided Design and 3D printing software to evaluate the durability of the implant, increase the surgical accuracy, and reduce surgical costs and risks. The large skull patch was designed by reverse engineering. The subtraction method was applied based on a healthy skull prototype. The large cranial implants on the two halves of the skull were asymmetrical and included fixation parts. Using the finite element method, the asymmetric defect skull model was simulated under intracranial pressures and a static load of 50 N placed at three positions. The results are shown through displacement, stress, and elastic deformation. The cranial implants were implanted, ensuring the material’s durability, and improving the patient’s aesthetics. In this study, a cranial implant design and evaluation method for large skull defects reduces the time and risk of surgery. Generous size skull pieces can be fabricated in compliance with specific design criteria. The design of the cranial implant met the basic operating conditions of the patient through the finite element method. The cranial implants were fabricated by injection molding and successfully implanted into the patient.

Data-Driven Proxy Modeling of Water Front Propagation in Porous Media

In the water flooding process, determining the location of the injected water front is as one of the most critical variables, which is the basis of many subsequent predictions. Despite the importance and use of this parameter in a vast range of flooding-related assessments, there are no alternative methods to traditional analytical modeling or time-consuming numerical 3D simulation for its determination. This study introduces a data-driven proxy modeling approach based on two powerful deep learning algorithms for real-time determination of the injected water front location on the grid scale. The developed proxy models have realized the possibility of modeling the location of the flow front by minimally using the data extracted from the numerical simulators and only relying on commonly available field data. The proposed proxy models successfully simulated the breakthrough time in production wells and water arrival time in certain reservoir grids in new blind scenarios.

Numerical simulation of 3D swirling flow of Maxwell nanomaterial with a binary chemical mechanism and nonlinear thermal radiation effects

The effect of activation energy on the 3D swirling flow of Maxwell nanomaterial has been addressed. The mathematical formulation is designed via nonlinear radiation and heat absorption/generation. The novel attributes of an irregular movement and thermophoresis are additionally preserved. Mass convective and thermal convective conditions are considered. Suitable transformations have been considered to convert PDEs into ODEs. The NDSolve technique is employed to obtain numerical simulations. Plots are generated to analyze the role of several influential variables on nondimensional nano-concentration and temperature fields. Moreover, rates of mass and heat transport are also analyzed through plots.

Generalizable Permeability Prediction of Digital Porous Media via a Novel Multi‐Scale 3D Convolutional Neural Network

AbstractSubsurface characterization is critical in understanding and controlling many natural and industrial processes including groundwater movement, oil extraction, and geological carbon dioxide sequestration. While recent advances in three‐dimensional (3D) imaging of core samples have enabled digital subsurface characterization, the exorbitant computational cost associated with direct numerical simulation in 3D remains a persistent challenge. In contrast, machine learning models are much more efficient, though their use in subsurface characterization is still in its infancy. Here, we introduce a novel 3D convolutional neural network (CNN) for end‐to‐end prediction of permeability, which is a fundamental characteristic of subsurface porous media. We show that increasing the dataset size and diversity, utilizing multi‐scale feature aggregation, and optimizing the network architecture elevate the model accuracy beyond that of existing state‐of‐the‐art 3D CNN models for permeability prediction. We demonstrate that the model is generalizable, and it is capable of predicting the permeability of previously unseen samples with an excellent accuracy.

A collapsing sandpile problem with nonlocal boundary condition

In this work, we continue our study on the sandpile model proposed by Igbida. We are particularly interested in the study of avalanches that occur on the surface of a pile of sand following a drying out. The main novelty here is that we do a theoretical and numerical analysis in the case of local and non-local boundaries conditions. We also present some results of numerical simulations in 2D.