In continuous steel casting, a tundish distributes molten steel that is supplied from a ladle to molds. The pattern of molten steel flow in the tundish influences the steel quality because functions such as inclusion separation and constant feed of molten steel are performed by using flow-control devices. In the present paper, a generative neural network system for predicting steel flow fields in a tundish with a variety of configurations of the dam and the weir is developed. The present artificial neural network system is trained to predict molten steel flow in a real-scale tundish by using information available from numerical simulations of water flow in a reduced-scale tundish counterpart. Prediction accuracy primarily depends on physical variables that make up training datasets. The size of the clipped flow field is another crucial factor for efficient, accurate learning.

A moving weir to reduce the time for grade transition is proposed. To investigate benefits of the proposed moving weir, tundish flow subject to various conditions of a moving weir was numerically investigated. First, an optimal travelling path of a horizontally moving weir was determined in a water model. Investigation of various cases shows that the shortest transition time is obtained when new molten steel is injected after the weir returns to its original position after a round-trip. Using this travelling path, the speed of the moving weir was investigated in a real-scale model to determine an optimal speed that stabilizes the surface height while the transition time is minimized. As a result, intermixing of steel with dissimilar grades has been reduced by 14.5 % by using the optimal conditions of the moving weir. Lastly, the performance of vertically moving weirs was assessed by comparing with that of the horizontal counterpart.

A computational method for GPU-accelerated fractional-step integration of incompressible Navier-Stokes equations based on the Alternating Direction Implicit (ADI) method is presented. Non-iterative, direct solution methods used in the semi-implicit fractional-step method take advantage of tridiagonal systems and Fourier transform whose solution can be computed using fast algorithms on a single GPU. However, when data is distributed to multiple GPUs, all-to-all matrix transposition is required, which increases computational cost significantly. In this work, a new strategy that does not require all-to-all transposition is proposed. The computational domain is divided in the wall-normal direction, and decoupled tridiagonal systems are obtained using Parallel Diagonal Dominant (PDD) and Parallel Partition (PPT) methods. An optimal batch size is determined to maximize the performance of PDD and PPT methods within a given amount of GPU memory. Strengths and weaknesses of this type of domain decomposition are investigated in comparison to conventional ways of dividing the domain along streamwise or spanwise directions. Using 8 NVIDIA Tesla P100 GPUs, the utility of the present method is demonstrated in a direct numerical simulation (DNS) of a canonical zero-pressure-gradient turbulent boundary layer and a DNS of a K-type boundary-layer transition on 1.4 billion grid cells.

Predictive capabilities of unsteady Reynolds-averaged Navier–Stokes (URANS) techniques using the k-omega shear stress transport and Spalart–Allmaras models are assessed for the simulation of turbulent boundary layers under unsteady adverse pressure gradients by comparing their results with direct numerical simulation (DNS) results. Simulations are conducted for separating and reattaching turbulent boundary layers under periodic adverse pressure gradients. Phase-wise comparisons of the velocity, the Reynolds stress, and the skin friction coefficient obtained by URANS simulations and DNS are carried out. URANS techniques are found to qualitatively well predict the formation of the separation bubble and the phase response of the shear layer height, while they predict earlier separation and a larger recirculation bubble compared with those in DNS. Phase responses of the skin friction predicted by URANS simulations are found not to be an accurate indication of flow separation and reattachment of the turbulent boundary layer. The main causes of discrepancies among DNS and URANS results in the near-wall region are attributed to the different anisotropy of the Reynolds stress, which can be characterized by a barycentric map.

A simultaneous-approximation term is a non-reflecting boundary condition that is usually accompanied by summation-by-parts schemes for provable time stability. While a high-order convective flux based on reconstruction is often employed in a finite-volume method for compressible turbulent flow, finite-volume methods with the summation-by-parts property involve either equally weighted averaging or the second-order central flux for convective fluxes. In the present study, a cell-centered finite-volume method for compressible Naiver–Stokes equations was developed by combining a simultaneous-approximation term based on extrapolation and a low-dissipative discretization method without the summation-by-parts property. Direct numerical simulations and a large eddy simulation show that the resultant combination leads to comparable non-reflecting performance to that of the summation-by-parts scheme combined with the simultaneous-approximation term reported in the literature. Furthermore, a characteristic boundary condition was implemented for the present method, and its performance was compared with that of the simultaneous-approximation term for a direct numerical simulation and a large eddy simulation to show that the simultaneous-approximation term better maintained the average target pressure at the compressible flow outlet, which is useful for turbomachinery and aerodynamic applications, while the characteristic boundary condition better preserved the flow field near the outlet.

A recursive filtering technique is developed to improve the computational efficiency of explicit-filter large-eddy simulation in highly parallelized computational environments. In parallel computations on a partitioned domain, unlike in non-recursive explicit filtering in which the number of ghost cell layers for storing neighbor cell values to ensure communication with neighbor partitions is increased rapidly as the stencil of the filter becomes wider, the present recursive filtering technique requires only a single layer of ghost cells for storing immediate neighbor cell values regardless of the stencil width of the filter. A generalized algorithm for construction of recursive filters with desired filter widths is developed. The computational efficiency of the proposed recursive filtering technique over the conventional non-recursive broad-band filtering techniques in terms of memory usage and computational time is presented.

A predictive convolutional neural network is developed to predict the future of three-dimensional unsteady wake flow from past information of flow velocity and pressure. The developed network is found to be capable of predicting vortex dynamics at distinctive flow regimes with flow structures at different scales. Mechanisms of the network on predicting vortex dynamics at two distinctive flow regimes, the mode-B shedding regime and the turbulent wake regime, are investigated. Information in feature maps of the network is visualized and quantitatively assessed to investigate the encoded flow structures. A Fourier analysis is conducted to investigate the mechanisms of the network on learning fluid motions with distinctive flow scales. The transformation of information from the input to prediction layers of the network is tracked to examine how the network transforms the input information for prediction. Structural similarities among feature maps in the network are evaluated to reduce the number of feature maps containing redundant flow structures, which allows reduction of the size of the network without affecting prediction performance.

A new numerical method to solve three-dimensional wave equations in media with arbitrarily-shaped interfaces on a Cartesian grid is proposed. The present method aims to achieve two objectives to simulate wave propagation through realistic geometries: (1) handling wave interaction at the interface with high ratios of acoustic material properties and (2) treating complex geometries involving both smooth and non-smooth interfaces. To achieve the first objective, the present method extends the solution smoothly across the interface in the direction normal to the interface. A cell layer of ghost points on each side of the interface is used to enforce interface conditions, which support not only reflection but also transmission of incident waves. Ghost-point values are determined by applying a local coordinate-transform and a weighted least squares error method, which suppress numerical instabilities. To achieve the second objective, the interface geometry is approximated using an unstructured surface mesh, which does not require analytic information about the interface geometry. Finally, the accuracy and effectiveness of the present method are validated and demonstrated for wave propagation over or through several two-dimensional and three-dimensional obstacles.

A ghost-cell immersed boundary method for unified simulations of flow over finite- and zero-thickness moving bodies at large Courant-Friedrichs-Lewy (CFL) numbers is presented. In order to handle such bodies in a unified manner, algorithms for interface construction and cell demarcation are proposed. The main challenge in treating zero-thickness bodies is to maintain sharpness and accuracy even at large CFL numbers with diminished spurious force oscillations. Thus, the effect of large CFL numbers on the solution accuracy of fluid-structure interaction (FSI) problems involving zero-thickness bodies is investigated and necessary treatments to preserve solution accuracy even at large CFL numbers are suggested. The present study suggests two treatments which are important in preserving the accuracy and stability of the solution: backward time integration for computational cells called ‘swept-cells’ and pressure boundary condition with mass conservation. Composite implicit time integration for the dynamic equation of a thin elastic structure is employed for a stable simulation of FSI at large CFL numbers. By using large time step sizes, the present method not only enhances computational efficiency, but also suppresses spurious force oscillations while maintaining the sharpness of an infinitesimally thin body. The efficacy and accuracy of the present method are examined through numerical examples.

The accuracy and the applicability of the parallel diagonal dominant (PDD) algorithm are explored for highly scalable computation of the incompressible Navier-Stokes equations which are integrated using a fully-implicit fractional-step method in parallel computational environments. The PDD algorithm is known to be applicable only for an evenly diagonal dominant matrix. In the present study, however, it is shown mathematically that the PDD algorithm is utilizable even for non-diagonal dominant matrices derived from discretization of incompressible momentum equations. The order of accuracy and the error characteristics are investigated in detail in terms of the Courant-Friedrichs-Lewy (CFL) number and the grid spacing by conducting simulations of decaying vortices in both two and three dimensions, flow in a lid-driven cavity, and flow over a circular cylinder. In order to reduce communication cost, which is one of bottlenecks in parallel computation, an aggregative data communication method is combined with the PDD algorithm. Parallel performance of the present PDD-based method is investigated by measuring the speedup, efficiency, overhead, and serial fraction.