Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes equations govern compressible flows and allow for complex phenomena like turbulence and shocks. Despite tremendous progress in hardware and software, capturing the smallest length-scales in fluid flows still introduces prohibitive computational cost for real-life applications. We are currently witnessing a paradigm shift towards machine learning supported design of numerical schemes as a means to tackle aforementioned problem. While prior work has explored differentiable algorithms for one- or two-dimensional incompressible fluid flows, we present a fully-differentiable three-dimensional framework for the computation of compressible fluid flows using high-order state-of-the-art numerical methods. Firstly, we demonstrate the efficiency of our solver by computing classical two- and three-dimensional test cases, including strong shocks and transition to turbulence. Secondly, and more importantly, our framework allows for end-to-end optimization to improve existing numerical schemes inside computational fluid dynamics algorithms. In particular, we are using neural networks to substitute a conventional numerical flux function.
翻译:液流是自然和工程学科中无处不在的流体流体。 可靠的液体计算是一个长期挑战, 原因是在多个时空尺度上的非线性互动。 压缩的纳维尔- 斯托克方程式控制着压缩流体, 并允许出现动荡和冲击等复杂现象。 尽管在硬件和软件上取得了巨大进步, 捕捉流体中最小的长度尺度仍然为现实生活应用带来了令人望而却步的计算成本。 我们目前正在目睹一种范式的转变, 转向机器学习支持的数字方法的设计, 作为解决上述问题的手段。 尽管先前的工作已经探索了一或二维不可压缩流体的可不同算法,但我们展示了一个完全可区别的三维框架, 用于使用高阶状态、 先进的数字方法计算可压缩流体流。 首先, 我们通过计算经典的二维和三维测试案例, 包括强震荡和向动荡过渡, 展示了我们解决问题者的效率。 第二, 更重要的是, 我们的框架允许最终的优化, 来改进现有的计算流体动力动态系统。 特别是, 我们使用常规的变数变的网络。