Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session Q41: Advances in CFD Algorithms II |
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Chair: Kursat Kara, Oklahoma State University Room: 6c |
Tuesday, November 26, 2019 7:45AM - 7:58AM |
Q41.00001: Using Evolutionary Neural Networks to Adapt the Jacobi Iterative Method for the Pressure Poisson Equation in a Multiphase Flow Tianrui Xiang, yipeng Shi, Xiang Yang We utilize evolutionary neural networks (ENNs) to determine a set of relaxation factors for the Jacobi iterative method, which is subsequently used to solve the pressure Poisson equation of a multiphase flow. The density of the fluid and the gas differ by a factor of ~1000. An iterative method usually needs to be adapted to account for the large density different in the field, which usually involves a long process of trial and error. In this talk, we show that ENNs could shorten this process. The iterative method we adapt is the Jacobi method. This method is embarrassingly parallel, and converges at a reasonable rate if employing a set of appropriately picked relaxation factors. Our ENN uses the iterative solution at one instance as the input, and determines the relaxation factor for the next iteration. Despite the local nature of our input to the neural network, we show that the results of the ENN is very close to the global optimum. [Preview Abstract] |
Tuesday, November 26, 2019 7:58AM - 8:11AM |
Q41.00002: Automatic differentiation of a spectral difference code for sensitivity analysis Jose I. Cardesa, Christophe Airiau The computational fluid dynamics code JAGUAR, developed jointly by ONERA (Toulouse) and CERFACS, is a high-order code based on spectral differences and intended for unsteady aerodynamic simulations. In order to extend its use for shape optimization and flow control, it is convenient to adapt the code so that computing flow sensitivities is an efficient yet flexible process that can be adapted to very different problems. For this reason, a fully discrete approach was chosen that relies on automatic differentiation. A test case was analyzed to validate our approach in an unsteady problem, allowing us to identify key modifications to be implemented on the code so as to streamline the differentiation process and ease its replication in other problems. Tangent and adjoint modes were used to differentiate the parallel version of the code with TAPENADE and the adjoinable MPI library. Execution times and coding strategies will be provided to illustrate the benefits and drawbacks of the different approaches. [Preview Abstract] |
Tuesday, November 26, 2019 8:11AM - 8:24AM |
Q41.00003: Stability and Accuracy of Semi-Extrapolated Finite Difference Schemes Andrew Brandon, Sheila Whitman, Mikayla Feldbauer, Narshini Gunputh, Brendan Drachler, Carter Alexander, Lucas Wilkins When numerically solving partial differential equations, finite difference methods are a popular choice. Several factors come into play when choosing a finite difference method, such as stability, accuracy, and computational cost. In response to the small stability regions of explicit methods and the computational cost of implicit methods, we've developed a novel discretization technique called semi-extrapolation. Semi-extrapolation generates explicit schemes from implicit schemes by applying extrapolation in an unconventional fashion. Unlike extrapolation, which can severely curtail stability, semi-extrapolation can improve stability, as compared to analogous explicit methods. Furthermore, semi-extrapolation can have unexpected effects on accuracy. In this presentation, the concept of semi-extrapolation will be introduced and two semi-extrapolated discretizations of the Advection-Diffusion Equation will be discussed. Then, the accuracies and stabilities of these semi-extrapolated discretizations will be compared to the accuracies and stabilities of analogous mainstream finite difference discretizations. [Preview Abstract] |
Tuesday, November 26, 2019 8:24AM - 8:37AM |
Q41.00004: Solving the Navier-Stokes governing equations through quantum computing Frank Gaitan We present a quantum algorithm that solves an arbitrary set of coupled non-linear partial differential equations and show how it can be used to solve the governing equations for a Navier-Stokes fluid. To test the algorithm we examine the problem of inviscid, compressible flow through a convergent-divergent nozzle. We numerically simulate application of the algorithm to find the steady-state flow when a shock-wave is and is not present in the divergent part of the nozzle. In each case excellent agreement is found between the output of the quantum simulation and the exact analytical solution, with the simulation successfully capturing the shock-wave in the latter case. We compare the computational cost of this quantum algorithm to that of deterministic and random classical algorithms; discuss future applications, as well as the potential long-term significance of quantum computing for the fluid dynamics community. [Preview Abstract] |
Tuesday, November 26, 2019 8:37AM - 8:50AM |
Q41.00005: A finite volume scheme for stochastic PDEs in the context of fluctuating hydrodynamics Sergio P. Perez, Antonio Russo, Miguel A. Duran-Olivencia, Peter Yatsyshin, Jose A. Carrillo, Serafim Kalliadasis The description of soft matter systems out of equilibrium requires the inclusion of fluctuations in the standard hydrodynamic equations for the evolution of conserved quantities. The associated general framework was postulated phenomenologically by Landau et. al., yielding what is known as Landau-Lifshitz fluctuating hydrodynamics. However, the numerical applicability of the fluctuating hydrodynamics entails several challenges which still remain elusive. In particular, conservative fluctuations, i.e. stochastic fluxes under the gradient operator, need to be properly accounted for. Besides, even for the simplest limit of these equations (which corresponds to the stochastic diffusion equation), the presence of a normally-distributed flux in the time-evolution equation for the density involves non-positive solutions, which are clearly unphysical. Hence the need for a robust method capable of handling stochastic fluctuations properly. Here we present a finite-volume scheme for stochastic gradient flows with nonlinear energy functionals, based on a hybrid upwind-central discretisation of both the deterministic and stochastic fluxes. The positivity of the density is ensured by an innovative time-adapting procedure based on the concept of Brownian trees. We exemplify the applicability and versatility of our method by solving the FH in a wide spectrum of physical settings. [Preview Abstract] |
Tuesday, November 26, 2019 8:50AM - 9:03AM |
Q41.00006: A symbolic regression approach for the development of high accuracy defect correction schemes Harsha Vaddireddy, Omer San Discrete equations are used to solve partial differential equations. Using higher order numerical schemes, we can traditionally reduce the number of grid points while preserving similar level of accuracy. Although high accurate numerical schemes can be constructed by using higher order polynomials, symmetry preservation, Padé approximation or Richardson extrapolation, it is well known that simple schemes sometimes completely eliminate the induced numerical errors when discretization parameters are chosen appropriately (e.g., dt = dx/a for the first order Euler upwind scheme solving the linear wave equation). Furthermore, closure approaches are often introduced to account for nonlinear interactions in discrete models. To this end, we introduce a modular symbolic regression framework for finding optimal parameters, defect correction or closure terms, if necessary, to improve the accuracy of the underlying numerical procedures. Several examples are conducted to assess the feasibility of the proposed approach. [Preview Abstract] |
Tuesday, November 26, 2019 9:03AM - 9:16AM |
Q41.00007: An Unconditionally Energy-Stable Scheme for Incompressible Flows with Outflow/Open Boundaries Suchuan Dong, Xiaoyu Liu We present an unconditionally energy-stable scheme for simulating incompressible flows on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a rotational velocity correction type strategy, and the adoption of the auxiliary variable simplifies the numerical treatment for the open boundary conditions. The scheme admits a discrete energy stability property, irrespective of the time step sizes. Within each time step the scheme entails the computation of two velocity fields and two pressure fields, by solving an individual de-coupled Helmholtz (including Poisson) type equation with a constant pre-computable coefficient matrix for each of these field variables. The auxiliary variable, being a scalar number, is given by a well-defined explicit formula within a time step, which ensures the positivity of its computed values. We present numerical results with several flows involving outflow/open boundaries in regimes where the backflow instability becomes severe to demonstrate the performance of the method and its stability at large time step sizes. [Preview Abstract] |
Tuesday, November 26, 2019 9:16AM - 9:29AM |
Q41.00008: Spectral Methods for Time Series Prediction with Application to Fluid Flows Henning Lange, Steven Brunton, Nathan Kutz Forecasting the behavior of complex dynamical systems has a rich history in fluid dynamics. Here, we propose spectral forecasting algorithms for linear as well as non-linear ergodic dynamical systems. For linear (and slightly non-linear) systems, we propose an algorithm that exploits the relationship between the discrete Fourier Transform (DFT) and the squared error as a function of model parameters, and we break the periodicity assumptions inherent to the DFT by making use of gradient descent. Because of its similarities to the DFT, we refer to this algorithm as the Predictive Fourier Decomposition. Furthermore, for non-linear dynamical systems. we introduce a second algorithm that performs a frequency decomposition in a non-linear basis which is inspired by Koopman theory, which we refer to as Predictive Koopman Decomposition. The resulting algorithm jointly learns oscillatory non-linear basis functions and a least-squares fit to the signal. We will show that the Predictive Koopman Decomposition allows for forecasting of some signals with infinite frequency spectra with which the Predictive Fourier Decomposition struggles. The algorithms are evaluated in the context of predicting signals in the realms of power systems, meteorology and turbulent flow. [Preview Abstract] |
Tuesday, November 26, 2019 9:29AM - 9:42AM |
Q41.00009: On preserving accuracy of underlying discretization in overset meshes for incompressible flow Ashesh Sharma, Shreyas Ananthan, Michael Sprague, Jayanarayanan Sitaraman To accurately model the flow dynamics around wind turbines, it is crucial to capture well the many complex moving geometries involved. The need to resolve flow structures around these moving components motivates our choice of overset grids. Exchange of solution between the overlapping meshes is at the core of any overset framework. For incompressible-flow solvers, the associated linear systems arising at each time step can be solved in a coupled or a decoupled and iterative manner. In the former, monolithic linear systems are assembled and the overlapping meshes are coupled through constraint equations. In a decoupled solve, linear systems are created for each mesh, and information is exchanged at overset interfaces as a separate step after the governing equations have been solved on the individual meshes. This work examines cost and accuracy comparisons between overset coupled and decoupled solves using elliptic and hyperbolic systems representative of the incompressible Navier-Stokes equations. [Preview Abstract] |
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