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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Neural networks for determining the vector normal to the surface in CFD, LBM and CA applications
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Neural networks for determining the vector normal to the surface in CFD, LBM and CA applications

机译：用于在CFD，LBM和CA应用中确定垂直于表面的矢量的神经网络

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Purpose - The well-known discrete methods of computational fluid dynamics (CFD), lattice Boltzmann method (LBM), cellular automata (CA), volume-of-fluid (VoF) and others rely on several parameters describing the boundary or the surface. Some of them are vector normal to the surface, coordinates of the point on the surface and the curvature. They are necessary for the reconstruction of the real surface (boundary) based on the values of the volume fractions of several cells. However, the simple methods commonly used for calculations of the vector normal to the surface are of unsatisfactory accuracy. In light of this, the purpose of this paper is to demonstrate a more accurate method for determining the vector normal to the surface. Design/methodology/approach - Based on the thesis that information about the volume fractions of the 3 × 3 cell block should be enough for normal vector determination, a neural network (NN) was proposed for use in the paper. The normal vector and the volume fractions of the cells themselves can be defined on the basis of such variables as the location of the center and the radius of the circumference. Therefore, the NN is proposed to solve the inverse problem - to determine the normal vector based on known values of volume fractions. Volume fractions are inputs of NNs, while the normal vector is their output. Over a thousand variants of the surface location, orientations of the normal vector and curvatures were prepared for volume fraction calculations; their results were used for training, validating and testing the NNs. Findings - The simplest NN with one neuron in the hidden layer shows better results than other commonly used methods, and an NN with four neurons produces results with errors below 1° relative to the orientation of the normal vector; for several cases, it proven to be more accurate by an order of magnitude. Practical implications - The method can be used in the CFD, LBM, CA, VoF and other discrete computational methods. The more precise normal vector allows for a more accurate determination of the points on the surface and curvature in further calculations via the surface or interface tracking method. The paper contains the data for the practical application of developed NNs. The method is limited to regular square or cuboid lattices. Originality value - The paper presents an original implementation of NNs for normal vector calculation connected with CFD, LBM and other application for fluid flow with free surface or phase transformation.
机译：目的-众所周知的计算流体力学（CFD），格子玻尔兹曼方法（LBM），细胞自动机（CA），流体体积（VoF）等离散方法依赖于描述边界或表面的几个参数。其中一些是垂直于曲面的矢量，曲面上点的坐标和曲率。它们是基于几个单元的体积分数的值重建实际表面（边界）所必需的。但是，通常用于计算垂直于表面的矢量的简单方法的精度并不令人满意。有鉴于此，本文的目的是演示一种更准确的方法来确定垂直于表面的矢量。设计/方法/方法-基于有关3×3细胞块体积分数的信息应足以确定法向量的论点，提出了一种神经网络（NN）用于本文。可以基于诸如中心的位置和周长的半径之类的变量来定义单元格本身的法线向量和体积分数。因此，提出了NN来解决反问题-基于体积分数的已知值确定法线向量。体积分数是神经网络的输入，而法线向量是它们的输出。准备了上千种表面位置，法向矢量和曲率的方向以进行体积分数计算。他们的结果用于训练，验证和测试神经网络。结果-在隐藏层中具有一个神经元的最简单NN显示出比其他常用方法更好的结果，而具有四个神经元的NN产生的结果相对于法向矢量的方向的误差小于1°；在某些情况下，它被证明更精确一个数量级。实际意义-该方法可用于CFD，LBM，CA，VoF和其他离散计算方法。更精确的法向矢量允许在通过表面或界面跟踪方法进行的进一步计算中更精确地确定表面上的点和曲率。本文包含了开发的神经网络的实际应用数据。该方法仅限于规则的正方形或长方体格子。原创性值-本文提出了用于法向矢量计算的NN的原始实现，与CFD，LBM和其他用于具有自由表面或相变的流体流动的应用有关。

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