In Eulerian methods, the simulation of an incompressible fluid field requires a pressure field solution, which takes a large amount of time and computation resources to solve a large coarse linear system. The pressure solver has two mathematical features. The first is that it obtains the pressure solution from a velocity divergence distribution in high-dimensional space. The second is that the pressure is iteratively solved in the projection step. Based on these two features, we investigate a convolutional-based neural network, which learns to map the fluid quantities to pressure solution iteratively by inferring from multiple grid scales. Our proposed network extracts features from multiple scales and then aligns them to obtain a pressure field in the original resolution. We trim our network structure to be compact and fast and design it to be iterative like to improve performance. Our approach requires less computation cost, while it achieves comparable performance with recently proposed data-driven methods. Our method can easily be parallelized in GPU devices, and we demonstrate its speed-up ability with the fluid field in larger input scenes.

在欧拉方法中，不可压缩流场的模拟需要压力场解，这需要大量时间和计算资源才能解决大型粗线性系统。压力求解器具有两个数学特征。首先是它从高维空间中的速度散度分布中获得压力解。第二个是在投影步骤中迭代求解压力。基于这两个特征，我们研究了基于卷积的神经网络，该网络通过从多个网格比例尺推断来学习将流体量迭代映射到压力解。我们提出的网络从多个比例尺中提取特征，然后将它们对齐以获得原始分辨率的压力场。我们调整网络结构使其紧凑，快速，并进行迭代式设计以提高性能。我们的方法需要较少的计算成本，同时可以达到与最近提出的数据驱动方法相当的性能。我们的方法可以很容易地在GPU设备中并行化，并且在较大的输入场景中，我们可以通过流场证明其加速能力。