Tree-based Local Mesh Refinement for Compressible Multiphase Flows

This study is aimed at developing a novel computational framework that seamlessly incorporates the feedback forcing model and adaptive mesh refinement mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) approach, so that challenging problems, including the interactions between flowing fluids and moving objects, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces are fully exhibited. Additionally, the "bubble' function is employed in the local mesh refinement process, so that the solution of second order accuracy at newly generated nodes can be obtained only by the spatial interpolation but no temporal interpolation. Focusing on both steady and unsteady flow around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present AMR IB-LBM approach.

The extreme conditions experienced in hypersonic flight can be difficult to reproduce in ground test facilities. As such, the use of computational simulations is vital in the design of Thermal Protection Systems (TPSs) for hypersonic vehicles. A relatively recent paradigm within Computational Fluid Dynamics (CFD) is to discretise the space around a vehicle using the strand/Cartesian Adaptive Mesh Refinement (AMR) technique, which requires minimal user input, with much of the process automated. This techniques combines a strand'' mesh, grown from a discretised surface, in the near-body region with an adaptive Cartesian mesh in the off-body region. This technique could be useful in the assessment of TPSs, where ablating surfaces and flexible TPSs require the mesh to be updated as the shape of the body changes. To this end, a prototype strand/Cartesian AMR solver has been created using the AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework. A patch integrator within AMROC has been extended to include Park's two-temperature model in order to model the thermochemical nonequilibrium present in hypersonic flows. A mapped spatial integration scheme has been developed along with strand meshing techniques in order to discretise the near-body domain using an input surface. Overset algorithms have been implemented to join the domains. The design of off-body and near-body solvers and the overset algorithms are presented along with a series of test cases that aim to verify and validate the hypersonic 2D/axisymmetric strand/Cartesian AMR solver. Shocktube results are compared with those from the literature, and code-to-code comparisons are carried out. The hypersonic model is validated using comparisons with Lobb's hypersonic sphere experiments, and the heat flux results are validated using data from a high-enthalpy shock tunnel experiment. The results indicate that the strand/Cartesian AMR technique could be used to accurately simulate vehicles in hypersonic flows.

Full particle simulation of the plasma sheet using adaptive mesh refinement technique

The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively with advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.

Star formation with 3-D adaptive mesh refinement: the collapse and fragmentation of molecular clouds

A GRP-based high resolution ghost fluid method for compressible multi-medium fluid flows I: One-dimensional case

In this paper we study numerically blow-up solutions of elliptic equations with nonlinear dynamical boundary conditions. First, we formulate a result for blow-up, when dynamical boundary condition is posed on the part of the boundary. Next, by semidiscretization, we obtain a system of ordinary differential equations (ODEs), the solution of which also blows up. Under certain assumptions we prove that the numerical blow-up time converges to the corresponding real blow-up time, when the mesh size goes to zero. We investigate numerically the blow-up set (BUS) and the blow-up rate. Numerical experiments with local mesh refinement technique are also discussed.

Three-dimensional forward modeling is a challenge for geometrically complex magnetotellurics (MT) problems. We present a new edge-based finite-element algorithm using an unstructured mesh for accurately and efficiently simulating 3D MT responses. The electric field curl-curl equation in the frequency domain was used to deduce the H (curl) variation weak form of the MT forward problem, the Galerkin rule was used to derive a linear finite-element equation on the linear-edge tetrahedroid space, and, finally, a BI-CGSTAB solver was used to estimate the unknown electric fields. A local mesh refinement technique in the neighbor of the measuring MT stations was used to greatly improve the accuracies of the numerical solutions. Four synthetic models validated the powerful performance of our algorithms. We believe that our method will effectively contribute to processing more complex MT studies.

A novel CFD approach based on adaptive mesh refinement (AMR) technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting (THINC/SW) scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.

A new numerical method based on the ghost fluid method was developed for compressible two-phase flows; the idea of adaptive mesh refinement with multigrid was implemented in the method. In the method, interpolation techniques between multiple grids near interfaces were also proposed. The present techniques are effective in diminishing the numerical instability caused by the discontinuity of physical variables across the interfaces. The bubble collapse induced by the interaction of an incident shock with a gas bubble in water was simulated with the present multigrid ghost fluid method. We have succeeded in capturing the fine interface and vortex structure during the collapsing and rebounding stage. The mass conservation is improved with the adaptive mesh refinement combined with the hybrid particle level set method. Also, the interaction of an incident shock wave with a gas bubble near a deformable boundary was simulated successfully with the method in which the motions of three phases, i.e., the gas inside the bubble, the ambient liquid, and the wall material, are taken into consideration.

This paper presents a numerical sketch-based methodology to achieve optimal product design solutions, bridging the gap between initial conceptual sketches and advanced engineering analyses. The proposed approach enables the transformation of simple hand-drawn sketches into digital models suitable for complex computational simulations and design optimization. Using computer vision algorithms, sketches are processed to generate digital design components that serve as inputs for Finite Element Analysis (FEA). In order to further enhance the overall design process, topology optimization (TO) is also performed, iteratively refining the geometry to achieve optimal material distribution for improved structural performance. Additionally, Adaptive Mesh Refinement (AMR) techniques are applied to ensure computational efficiency and accuracy by dynamically refining the mesh in regions of high complexity or stress concentration. The synergy of sketch-based modeling, FEA, TO, and AMR demonstrates significant potential in reducing design cycles while maintaining high-performance standards. Finally, it should be noted that the proposed pipeline consists of a fully automated procedure, hence it could reduce the learning curve for the designers, enabling companies to onboard employees faster and integrate advanced design techniques into their workflows without extensive training. The above-mentioned modules render the introduced approach particularly suitable for applications in product design development that can be utilized in several industries like mechanical, manufacturing, and furniture.

This article discusses contemporary strategies to deal with immersed boundary (IB) frameworks useful for analyzing flow–structure interaction in complex settings. It focuses on immense advancements in various fields: biology, oscillation of structures due to fluid flow, deformable materials, thermal processes, settling particles, multiphase systems, and sound propagation. The discussion also involves a review of techniques addressing moving boundary conditions at complex interfaces. Evaluating practical examples and theoretical challenges that have been addressed by these frameworks are another focus of the article. Important results highlight the integration of IB methods with adaptive mesh refinement and high-order accuracy techniques, which enormously improve computational efficiency and precision in modeling complex solid–fluid interactions. The article also describes the evolution of IB methodologies in tackling problems of energy harvesting, bio-inspiration propulsion, and thermal-fluid coupling, which extends IB methodologies broadly in many scientific and industrial areas. More importantly, by bringing together different insights and paradigms from across disciplines, the study highlights the emerging trends in IB methodologies towards solving some of the most intricate challenges within the technical and scientific domains.

This study employs a coupled Volume of Fluid (VOF) and Discrete Phase Model (DPM) approach along with the Adaptive Mesh Refinement (AMR) technique to capture the transient topological behaviour of the slag-metal-air interface in a 260-ton top-bottom combined blowing converter. The droplet splashing patterns and mechanisms are investigated both qualitatively and quantitatively based on blowing number theory. The results indicate that droplet formation arises from the combined effects of shear stress and surface waves. The two resulting types of splashes are designated as ‘impact-induced splashing’ and ‘wave-induced splashing’. Droplet splashing exhibited two distinct modes: ‘dropping’ and ‘swarming’. The slag layer demonstrated inhibitory effects on the ‘swarming’ splashing pattern. The droplet generation rate decreases with increasing slag layer thickness, air-slag surface tension and slag viscosity. Furthermore, the morphology of the impact cavities significantly influences splashing behavior, while the slag layer tend to suppress cavities formation.

The finite-difference time-domain (FDTD) method is combined with an adaptive mesh refinement (AMR) technique, to achieve a fast, time-domain solver for Maxwell's equations (AMR-FDTD), based on a three-dimensional moving/rotating Cartesian mesh. This combination allows the proposed solver to adapt to the problem at hand, optimally distributing computational resources in a given domain as needed, by recursively refining a coarse grid in regions of large over time gradient of electromagnetic field energy. Several applications of the method to the analysis of microwave circuit geometries demonstrate its salient features and its outstanding efficiency as a microwave computer-aided design tool.

We study how the propagation speed of interfaces in the Allen-Cahn phase field model for phase transformations in solids consisting of the elasticity equations and the Allen-Cahn equation depends on two parameters of the model. The two parameters control the interface energy and the interface width but change also the interface speed. To this end we derive an asymptotic expansion of second order for the interface speed, called the kinetic relation, and prove that it is uniformly valid in both parameters. As a consequence we show that the model error is proportional to the interface width divided by the interface energy. We conclude that simulations of interfaces with low interface energy based on this model require a very small interface width, implying a large numerical effort. Effective simulations thus need adaptive mesh refinement or other advanced techniques. This version of the paper contains the proofs of Theorem 4.5 and Lemma 5.8, which are omitted in the version published in Continuum Mechanics and Thermodynamics.