Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session H18: Computational Fluid Dynamics: Algorithms I 
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Chair: Dorrin Jaranbashi, Texas A&M University Room: North 131 C 
Monday, November 22, 2021 8:00AM  8:13AM 
H18.00001: Local Extreme Learning Machines: A Neural Network Based Spectral ElementLike Method Suchuan Dong, Zongwei Li Existing deep neural networkbased methods for solving boundary/initialvalue problems suffer from several drawbacks (e.g. lack of convergence with a certain convergence rate, limited accuracy, extremely high computational cost) that make them numerically less than satisfactory and computationally uncompetitive. Here we present a neural networkbased method that has largely overcome these drawbacks. This method, termed local extreme learning machines (locELM), combines three ideas: extreme learning machines, domain decomposition, and local neural networks. The field solution on each subdomain is represented by a local feedforward neural network, and C^{k} continuity conditions are imposed on the subdomain boundaries. The hiddenlayer coefficients of the local neural networks are preset to random values and fixed, and only the weight coefficients in the output layers are trainable parameters. The overall neural network is trained by a linear or nonlinear least squares computation, not by the backpropagation (or gradient descent) type algorithms. The current method exhibits a clear sense of convergence with respect to the degrees of freedom in the neural network. Its numerical errors typically decrease exponentially or nearly exponentially as the number of degrees of freedom (e.g. the number of trainable parameters, number of training data points) increases, which is reminiscent of the traditional spectral or spectral elementtype methods. LocELM far outperforms the deep Galerkin method (DGM) and the physics informed neural network (PINN) method in terms of the accuracy and computational cost (network training time). Its computational performance (accuracy/cost) is on par with the traditional finite element method (FEM), and outperforms FEM when the problem size becomes larger. These characteristics will be demonstrated for a number of problems. 
Monday, November 22, 2021 8:13AM  8:26AM 
H18.00002: Evolutional deep neural networks for accurate NavierStokes solutions and forecasts of turbulence Yifan Du, Tamer A Zaki Evolutional deep neural networks (EDNN) are introduced for accurate solution of nonlinear partial differential equations (Du, Y., & Zaki, T. A. (2021). arXiv preprint arXiv:2103.09959). Training is only required for EDNN to represent the initial condition. The network parameters are subsequently evolved, or marched, in time using the governing equations to provide accurate forecasts and without any further training. Boundary conditions are treated as hard constraints that are enforced by the network design and therefore are exactly satisfied. For the solution of NavierStokes equations, the divergencefree constraint is embedded into the network structure. The solution of the momentum equation is thus guaranteed to be solenoidal, which eliminates the computationally costly pressureprojection step. Since EDNN represents the solution in space and evolves in time, the network architecture is compact and requires relatively low memory. The evolutional nature of EDNN, where the parameters are updated using the equations rather than training within a specified time window, is suitable for forecasting the solutions of nonlinear chaotic systems, including turbulence, for indefinite time horizons. 
Monday, November 22, 2021 8:26AM  8:39AM 
H18.00003: A novel recursive unsupervised clustering MoE to represent flamelet tables Rohit Mishra, Sarvesh Mayilvahanan, Dorrin Jarrahbashi Flameletbased modeling has been extensively used to reduce the computational costs of combustion simulations. However, this method requires a large amount of storage that substantially increases the costs of combustion simulations in 3D. A novel recursive unsupervisedlearning based clustering method is introduced to predict the flamelet table. The proposed technique uses a Mixture of Experts (MoE) architecture involving specialized Deep Neural Networks (DNNs) trained on separate parts of the input space, which is subdivided using an unsupervised clustering algorithm. The models were trained and evaluated on a 4dimensional flamelet table and are tested apriori and aposteriori through 3D simulation of Sandia Flame D. Comparing the proposed method with the predictions of a Single Neural Network (SNN) model and standard interpolation method demonstrates significant improvement in predicting OH and NO mass fractions in different spatial locations. 
Monday, November 22, 2021 8:39AM  8:52AM 
H18.00004: Grid Convergence Index (GCI) Analysis of the Computational Mesh Resolution for Two Numerical Simulation Schemes for the LiquidGas Interfacial Reconstruction/Advection in Micron and Submicron Scales Reza Nazari, Adil Ansari, Ronald J Adrian, Richard Kirian, Marcus Herrmann We assessed the computational grid independence (GCI) [1] of two OpenFOAM builtin solvers to investigate the accuracy of their interfacial reconstruction and advection schemes in micron and submicron scales. For the case of a perturbed cylindrical column collapse [2], the flow is assumed to be transient, incompressible, and immiscible. The free surface is modeled with a compressive flux in the MULES [3] solver within the interFoam [3] solver while it is modeled with geometric fluxing in the isoAdvector [4] solver which is a subroutine of the interIsoFoam [5] solver. The two solvers, namely interFoam and interIsoFoam, allow for the simulation of the twophase Navier Stokes equations with a free surface. Adaptive Mesh Refinement (AMR) near the interface is used to better resolve the flow regions in the vicinity of the liquidgas interface. Since the surface tension is primarily responsible for generating an increased pressure inside the liquid, GCI analysis [1] was done on the average relative pressure over the simulation domain. For the test cases with the cylindrical column of about 12.5 microns in diameter, the observed order of convergence of the GCI analysis demonstrates a comparatively negligible dependence of the numerical simulation results on the computational grid beyond about half a micron. Moreover, a higher value of the observed order of convergence and smaller GCI error values for the interIsoFoam [5] solver shows a comparatively better capturing of the liquidgas interface by using geometric fluxing. 
Monday, November 22, 2021 8:52AM  9:05AM 
H18.00005: Adaptive chemistry reduction using Deep Neural Networks and Global Pathway Selection Rohit Mishra, Aaron Nelson, Dorrin Jarrahbashi Chemistry reduction is one of the main pillars of modern multidimensional combustion simulations. However, usually there is a tradeoff between the accuracy of the reduction model and the computational time. Many strategies have been developed in the past to avoid solving the complete set of reactions in a given kinetic mechanism. One of these strategies is the Global Pathway Selection (GPS). A novel adaptive GPS method is developed which creates multiple GPS skeletal mechanisms for short duration during combustion to better match the detailed chemistry prediction. The model not only predicts the combustion closer to detailed chemistry but also reduces the computational costs by removing species in regions of low activity. We also show how this technique can be used efficiently by implementing Deep Neural Networks (DNN) which avoids running GPS on the fly. The proposed scheme is validated with a 0D and 1D combustion simulation. 
Monday, November 22, 2021 9:05AM  9:18AM 
H18.00006: Robust, segregated time integration for direct numerical simulation of lowMach, variabledensity, turbulent flows Bryan W Reuter, Todd A Oliver, Robert D Moser

Monday, November 22, 2021 9:18AM  9:31AM 
H18.00007: Temporally Adaptive Conservative Scheme for Unsteady Compressible Flow Patrick Jenny, Valérie Kulka An adaptive conservative time integration scheme (ACTI) for compressible flow simulations is devised. A finite volume method is used, in which every cell employs a time step size which is some power of two times smaller than a global time step. By first advancing those cells with smaller time steps, this allows to use the already computed accumulated fluxes when the adjacent cells with larger time steps catch up. Conservation and periodic synchronization are thus guaranteed by construction; both important advantages of the new scheme (especially in the presence of shock waves) compared to previously proposed adaptive time stepping methods for compressible flow. Accuracy and computational speedup are demonstrated for challenging 1D and 2D test cases. Comparisons of ACTI results with an analytical solution and with results obtained without ACTI show excellent agreement. Although maximum wave speeds and/or cell sizes vary by several orders of magnitude throughout the computational domains, the CFL numbers employed by ACTI in each cell vary not more than by approximately a factor of two. Without ACTI, on the other hand, the CFL numbers are tiny in most of the cells. Since this results in a dramatic reduction of required flux computations, high speedup gains are achieved due to ACTI. 
Monday, November 22, 2021 9:31AM  9:44AM 
H18.00008: Predicting drag on rough surfaces by transfer learning of empirical correlations Sangseung Lee, Jiasheng Yang, Pourya Forooghi, Alexander Stroh, Shervin Bagheri In this presentation, we discuss how to model the drag on irregular rough surfaces using neural networks when only a limited amount of highfidelity data is available. We propose a transfer learning framework that pretrains neural networks with empirical correlations and finetunes them with a few direct numerical simulation data. We found that pretraining neural networks with empirical correlations can significantly improve the generalization ability of neural networks. The developed framework can be applied to applications where acquiring a large dataset is difficult, but empirical correlations have been reported. 
Monday, November 22, 2021 9:44AM  9:57AM 
H18.00009: A Novel Adaptive Spectral Method for Fluid Flow Simulations in Nonperiodic Domains Narsimha R Rapaka, Ravi Samtaney

Monday, November 22, 2021 9:57AM  10:10AM 
H18.00010: A Novel Adaptive Variational FullyEulerian Scheme for FluidStructure Interaction Biswajeet Rath, Xiaoyu Mao, Rajeev K Jaiman Explicit interface tracking and bodyfitted approaches pose numerical challenges for fluidstructure 
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