Mesoscopic Methods in Engineering and Science

Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics is usually insensitive to the details of the underlying microscopic interactions

Application of a Free-surface Immersed Boundary-lattice Boltzmann Modeling to Wave Forces Acting on a Breakwater

A novel free surface immersed boundary-lattice Boltzmann method for wave–structure interaction and hydrodynamic force estimation is introduced. First, the proposed model is applied to incident wave propagation in a shallow water zone. The wave–breakwater interactions and wave forces on a breakwater are then analysed using the method. The results agreed with those of Goda’s formulae, confirming that the proposed model has a high potential for application to complex analysis of coastal engineering problems

Numerical wave flume with Lattice Boltzmann Method for Wave Energy Converters

Based on Lattice Boltzmann Method, a free interface tracking model using volume of fraction (VOF) technique is built to explore the interaction of Oscillating Water Column (OWC) type of Wave Energy Converters (WECs) with waves. In the numerical wave flume, the momentum source is applied to generate incident waves and absorb reflected waves. After validation, one stationary OWC in the absence of Power take-off system (PTO) is then placed in the numerical wave flume to examine the performance of the numerical scheme. The simulation results show that the numerical stability is well achieved with the wave-structure interaction included and there is a strong vortex shedding at wall corner and nonlinearity with smaller amplitude in the present viscous flow model, compared with the linear potential flow solution

Simulation of casting filling process using the lattice Boltzmann method

Numerical simulation of casting filling process with complex shape is time-consuming. Compared with the traditional SOLA-VOF method, the lattice Boltzmann method (LBM) calculates the pressure field by particle distribution functions instead of the correction of the velocity and pressure fields, which greatly simplifies the calculation process. In addition, the LBM provides a flexible approach which can be easily parallelized. In this study, the LBM is employed to simulate casting filling process. An implementation of a volume-of-fluid (VOF) method within the lattice Boltzmann framework is proposed to capture the free surface of the casting filling process. A Smagorinsky large eddy simulation (LES) model is adopted to improve the numerical stability of the LBM. An adaptive time stepping technique is implemented to ensure an efficient and stable simulation. The model is validated by the experimental and simulation results of Campbell box filling process. The filling process of complex casting is simulated, and the result is compared with the filling process obtained by the SOLA-VOF method. The prediction accuracy and reliability of free surface profile is analysed

A numerical framework for simulating fluid-structure interaction phenomena

In this paper, a numerical tool able to solve fluid-structure interaction problems is proposed. The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. The Immersed Boundary method is used to account for the presence of an immersed solid in the lattice fluid background and to handle fluid-structure interface conditions, while a Volume-of-Fluid-based method is adopted to take trace of the evolution of the free surface. These ingredients are combined through a partitioned staggered explicit strategy, according to an efficient and accurate algorithm recently developed by the authors. The effectiveness of the proposed methodology is tested against two different cases. The former investigates the dam break phenomenon, involving the modeling of the free surface. The latter involves the vibration regime experienced by two highly deformable flapping flags obstructing a flow. A wide numerical campaign is carried out by computing the error in terms of interface energy artificially introduced at the fluid-solid interface. Moreover, the structure behavior is dissected by simulating scenarios characterized by different values of the Reynolds number. Present findings are compared to literature results, showing a very close agreement

A numerical framework for simulating fluid-structure interaction phenomena

In this paper, a numerical tool able to solve fluid-structure interaction problems is proposed. The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. The Immersed Boundary method is used to account for the presence of an immersed solid in the lattice fluidbackground and to handle fluid-structure interface conditions, while a Volume-of-Fluid-based method isadopted to take trace of the evolution of the free surface. These ingredients are combined through a partitioned staggered explicit strategy, according to an efficient and accurate algorithm recently developed by the authors. The effectiveness of the proposed methodology is tested against two different cases. The former investigates the dam break phenomenon, involving the modeling of the free surface. The latter involves the vibration regime experienced by two highly deformable flapping flags obstructing a flow. A wide numerical campaign is carried out by computing the error in terms of interface energy artificially introduced at the fluid-solid interface. Moreover, the structure behavior is dissected by simulating scenarios characterized by different values of the Reynolds number. Present findings are compared to literature results, showing a very close agreement.&nbsp

Analysis and comparison of boundary condition variants in the free-surface lattice Boltzmann method

The accuracy of the free-surface lattice Boltzmann method (FSLBM) depends significantly on the boundary condition employed at the free interface. Ideally, the chosen boundary condition balances the forces exerted by the liquid and gas pressure. Different variants of the same boundary condition are possible, depending on the number and choice of the particle distribution functions (PDFs) to which it is applied. This study analyzes and compares four variants, in which (i) the boundary condition is applied to all PDFs oriented in the opposite direction of the free interface's normal vector, including or (ii) excluding the central PDF. While these variants overwrite existing information, the boundary condition can also be applied (iii) to only missing PDFs without dropping available data or (iv) to only missing PDFs but at least three PDFs as suggested in the literature. It is shown that neither variant generally balances the forces exerted by the liquid and gas pressure at the free surface. The four variants' accuracy was compared in five different numerical experiments covering various applications. These include a standing gravity wave, a rectangular and cylindrical dam break, a rising Taylor bubble, and a droplet impacting a thin pool of liquid. Overall, variant (iii) was substantially more accurate than the other variants in the numerical experiments performed in this study

Hybrid Lattice-Boltzmann-Potential Flow Simulations of Turbulent Flow around Submerged Structures

We report on the development and validation of a 3D hybrid Lattice Boltzmann Model (LBM), with Large Eddy Simulation (LES), to simulate the interactions of incompressible turbulent flows with ocean structures. The LBM is based on a perturbation method, in which the velocity and pressure are expressed as the sum of an inviscid flow and a viscous perturbation. The far- to near-field flow is assumed to be inviscid and represented by potential flow theory, which can be efficiently modeled with a Boundary Element Method (BEM). The near-field perturbation flow around structures is modeled by the Navier–Stokes (NS) equations, based on a Lattice Boltzmann Method (LBM) with a Large Eddy Simulation (LES) of the turbulence. In the paper, we present the hybrid model formulation, in which a modified LBM collision operator is introduced to simulate the viscous perturbation flow, resulting in a novel perturbation LBM (pLBM) approach. The pLBM is then extended for the simulation of turbulence using the LES and a wall model to represent the viscous/turbulent sub-layer near solid boundaries. The hybrid model is first validated by simulating turbulent flows over a flat plate, for moderate to large Reynolds number values, Re ∈ [3.7×104;1.2×106]; the plate friction coefficient and near-field turbulence properties computed with the model are found to agree well with both experiments and direct NS simulations. We then simulate the flow past a NACA-0012 foil using a regular LBM-LES and the new hybrid pLBM-LES models with the wall model, for Re = 1.44 x 106. A good agreement is found for the computed lift and drag forces, and pressure distribution on the foil, with experiments and results of other numerical methods. Results obtained with the pLBM model are either nearly identical or slightly improved, relative to those of the standard LBM, but are obtained in a significantly smaller computational domain and hence at a much reduced computational cost, thus demonstrating the benefits of the new hybrid approach

Comparison of free-surface and conservative Allen-Cahn phase-field lattice Boltzmann method

This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen-Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vertical and (vi) oblique impact of a drop into a pool of liquid. Comparing the simulation results with either analytical models or experimental data from the literature, four major observations were made. Firstly, the PFLBM selected was able to simulate flows purely governed by surface tension with reasonable accuracy. Secondly, the FSLBM, a sharp interface model, generally requires a lower resolution than the PFLBM, a diffuse interface model. However, in the limit case of a standing wave, this was not observed. Thirdly, in simulations of a bubble moving in a liquid, the FSLBM accurately predicted the bubble's shape and rise velocity with low computational resolution. Finally, the PFLBM's accuracy is found to be sensitive to the choice of the model's mobility parameter and interface width

格子ボルツマン法による高効率な津波数値解析手法の開発

Tohoku University越村俊一課