The development of reconstruction methods has faced considerable challenges due to their inherent high dimensionality. In the present study, an innovative dimensionality reduction method aimed at mitigating these challenges by normalizing flow variables is proposed. Through our investigation, we demonstrate that a reconstruction method, specifically designed for a four-point stencil that is compatible with unstructured meshes, can be effectively represented by six two-dimensional functions. This key insight enables us to devise a visualization technique utilizing a single contour plot for the reconstruction method. Additionally, we establish that a single data set can adequately represent the reconstruction method, facilitating solution reconstruction through data set interpolation. By carefully evaluating the interpolation error, a data set of reasonable size yields sufficiently small interpolation errors. Notably, we uncover the possibility of extracting reconstruction methods from a trained artificial neural network (ANN). To gauge the impact of accumulated interpolation errors on solution quality, we conduct comprehensive analyses on four benchmark problems. Our results demonstrate that with a data set of sufficient size, the accumulated interpolation error becomes negligible, rendering the solution reconstruction by interpolating the extracted data set both accurate and cost-effective. The implications of our findings hold substantial promise for enhancing the efficiency and efficacy of reconstruction methods.

The potential of using an artificial neural network (ANN) to reconstruct the solution for CFD was investigated. From various ANN models, the multi-layer perceptron (MLP) model was adopted. At first, to examine the potential feasibility of using MLP for reconstruction, the numerical characteristics of MLP were investigated. Then training database α was created from the input-output relationship of WENO3, followed by database β (which maps the WENO3 input to the WENO7 output). A total of 6000 MLPs and 10000 MLPs were trained by Database α and β, respectively. To assess the capability of the present MLPs to handle strong discontinuity, the Sod problem was solved. Then the Shu-Osher problem was solved to evaluate the performance for a more general flow problem involving shocks and sinusoidal density waves. The well-trained MLP from database β, which yielded the most accurate solutions for both problems, was further assessed by solving the interacting blast waves problem and the supersonic channel test case on unstructured grids. The well-trained MLP yielded more accurate solutions for all test cases compared to WENO3 without extending the stencil. It was concluded that the MLP can potentially reconstruct the solution more accurately than existing reconstruction schemes.

In the present study, a new angular discretizationmethod, repulsive particle angular discretization (RPAD), is proposed for use with the three-dimensional radiative transfer equation (RTE). To discretize a solid angle as uniformly as possible, mutually repulsive particles on the unit sphere were introduced and directly used as radiation directions. To assess the uniformity of the radiation direction distributions of the RPAD and the other angular discretization methods, the minimum distances between control angles were compared. The assessment shows that the radiation direction distribution of the RPAD is the most uniform. The RPAD also achieved the most accurate first moment integral over the half solid angle. To assess various angular discretization methods including the RPAD in the three-dimensional spatial domain, they were adopted to solve two benchmark problems. The first benchmark problem is analysis of a cylindrical enclosure fill with a purely absorbing and emitting medium. In this problem, although the maximum radiative flux errors from the FTn FVM, IUSD, and RPAD were relatively similar, it was observed that the flux by the RPAD exhibits the least fluctuation for the varying surface direction with respect to the coordinate system. As a second benchmark problem, the rocket plume base heating was analyzed to assess the angular discretization methods in terms of pure scattering. It was observed that the maximum errors were smallest for the IUSD or RPAD, followed by the FTn FVM. However, the IUSD shows a relatively inaccurate radiative flux for a particular number of radiation directions. It was found that the RPAD proposed in the present study provides comparable or more accurate solutions for the three-dimensional RTE than the other angular discretization methods tested.

In the present study, a multi-layer perceptron (MLP) model was applied to flux reconstruction. To determine if an MLP can be used as a general numerical model, the numerical characteristics of an MLP were investigated. To train MLPs, a training database was constructed without any actual flow data and input vectors of the database were normalized to avoid numerical extrapolation. A total of 4,800 MLPs were trained and evaluated by numerically solving the Sod problem and the Shu-Osher problem. For the Sod problem, the well-trained MLP produced more accurate flow solutions than WENO3 and WENO5 did. In contrast, the solutions from the MLP were more accurate than those of WENO3 and less accurate than WENO5 for the Shu-Osher problem. Nonetheless, the MLP successfully captured a small wave peak on the specific grid that WENO3 and WENO5 did not capture.

In this paper, the hydrodynamic characteristics of a rim driven integrated thruster was numerically investigated. To consider the effect of cavitation phenomenon, multi-phase flow model and homogeneous mixture model were applied to the three dimensional incompressible RANS equations. To validate the numerical methods and the models adopted to the present study, the propeller P4381 was numerically analyzed and the numerical results and experimental one reached good agreement. The rim driven integrated thruster applied to the unmanned underwater vehicle at the water depth of 5m was numerically solved for various advance ratios. The flow field of the conventional thruster that has gap between the tip of the propeller and inner wall of the duct was also numerically solve and the results were compared to the results of the rim driven integrated thruster. As a result, it was revealed that both the rim driven integrated thruster and conventional thruster suffer from the cavitation phenomenon on the suction side of the propeller and the stator. It was also found that the difference of the thrust generated by the rim driven integrated thruster and conventional thruster is not significant whereas the difference of the torque could not be neglected. Finally, it was observed that the thrust and torque by thruster in the multi-phase flow was estimated to be smaller than those of single-phase flow.

In the present study, an amplifying neuron and attenuating neuron, which can be easily implemented into neural networks without any significant additional computational effort, are proposed. The activated output value is squared for the amplifying neuron, while the value becomes its reciprocal for the attenuating one. Theoretically, the order of neural networks increases when the amplifying neuron is placed in the hidden layer. The performance assessments of neural networks were conducted to verify that the amplifying and attenuating neurons enhance the performance of neural networks. From the numerical experiments, it was revealed that the neural networks that contain the amplifying and attenuating neurons yield more accurate results, compared to those without them.

Flow fields around a KARI-11-180 airfoil, SDM and transonic body are numerically simulated by using an unstructured meshes based compressible flow solver developed at KAIST. RANS equations are solved to analyse the flow fields and Roe's FDS method is adopted to evaluate convective fluxes. Turbulence effect of the flow fields is modeled by a SA model, SST model and gamma Re--(theta t) model. It is found that smaller drag coefficients are predicted for the KARI-11-180 airfoil when a transition phenomenon is considered and small deviations exist between CFD and EFD results. For the SDM, flow separation is observed at a leading edge and calculated aerodynamic properties show similar tendencies to experimental results. A shock wave on main wings of the transonic body is successfully captured by the present flow solver at a Mach number 0.9. Estimated pressure profiles by means of the present CFD method also agree well with those of wind tunnel results.