Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L31: Computational Fluid Dynamics Algorithms |
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Chair: Gretar Tryggvason, Johns Hopkins University Room: Georgia World Congress Center B403 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L31.00001: Abstract Withdrawn The task of filtering practical flow fields requires one to easily adapt scheme stencils, thus enabling accurate use near potentially challenging topological features (e.g., domain boundaries, sharp gradients, or grid discontinuities). Also important to consider is the stability of the resulting global filter operator, as well as the ability to preserve underlying conservational properties of the original field (e.g., integral quantities) (Wu and Meyers, Comp. Fluids, 48, 150-162, 2011). The current work thus introduces a simple and systematic method by which to generate boundary stencils for a target interior filtering scheme; overall spatial adaptivity is then attained via a domain decomposition perspective. Performance of the "cascade"-derived schemes are compared to traditional boundary methods and are assessed relative to a turbulent premixed flame example. The implementation of tunable and spectrally-sharp Pade filter formulations is considered, along with broader implications as relating to Large-Eddy Simulations (LES) and the stabilization of numerical CFD algorithms. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L31.00002: Invariant Numerical Schemes for Solution of Hyperbolic Partial Differential Equations Ersin Ozbenli, Prakash Vedula In this study, we extend our earlier work on Lie symmetry preservation in numerical schemes (Ozbenli and Vedula, JCP 349, 2017) and demonstrate the implementation of the proposed methods to more general problems including (but not limited to) hyperbolic PDEs. Considering non-invariant base numerical schemes that are obtained from compact schemes or defect correction procedures, we present a method to develop high order accurate invariant schemes that inherit Lie symmetry groups (such as translation, scaling, Galilean and projection groups) of underlying PDEs. Performance of the proposed method is evaluated through applications to numerical solution of linear/nonlinear advection equations and Euler equations for description of inviscid compressible flows (in 1D and 2D). For the case of Euler equations, we demonstrate the construction and performance of invariant forms of Lax-Friedrichs scheme and van Leer flux vector splitting scheme. Our preliminary results indicate that the invariant schemes often perform considerably better than their non-invariant counterparts. In particular it can be shown that invariant schemes often have significantly better performance with reference to error measures based on symmetries than standard (non-invariant) schemes. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L31.00003: Well-balanced finite-volume schemes for hydrodynamic equations with general free energy Sergio P. Perez, José A. Carrillo, Serafim Kalliadasis, Chi-Wang Shu The development of well-balanced numerical methods able to discretely preserve steady states of balance laws has attracted considerable attention since the first works nearly twenty years ago. Standard finite-volume approaches fail to accurately resolve the steady states from balance laws, in which the fluxes need to be exactly balanced with the source terms. To correct this deficiency, the well-balanced schemes are designed so as to discretely satisfy this balance when the steady state is reached. But well-balanced schemes for hydrodynamic equations with a general free energy have not been developed as of yet. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L31.00004: A fast pressure-correction method for incompressible flows over curved surfaces Abhiram Aithal, Antonio Ferrante In order to simulate turbulent flows over curved surfaces, the incompressible Navier-Stokes (NS) equations can be transformed to a more general formulation that allows them to be discretized in curved domains. This transformation leads to cross-derivatives in the expressions for Laplacian, advection, diffusion, and gradient operators. Further, the variable-coefficient Poisson equation for pressure is usually solved using an iterative solver at every timestep that leads to high computational costs. Thus, we have developed a new method to solve the incompressible NS equations in the orthogonal formulation. This has allowed us to develop a fast FFT-based Poisson solver which is at least forty-four times faster than the state-of-the-art multigrid-based iterative method. Provided the computational mesh satisfies the property of orthogonality, our numerical method can simulate flows over curved surfaces: surfaces of revolution (e.g., axisymmetric ramps) and surfaces of linear translation (e.g., curved ramps, bumps) with second-order accuracy. We present the results from convergence, verification and validation studies and the DNS results of flow over a smooth bump. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L31.00005: An extension of the ghost fluid method for multimaterial, compressible flows with surface tension Pedram Bigdelou, Praveen K Ramaprabhu We report on an extension of the ghost fluid method (GFM) to simulate multimaterial, compressible flows with surface tension between fluids. Our work builds on the earlier efforts of [1], who incorporated surface tension effects acting on an interface between separate compressible and incompressible materials. In our extension, both fluids are compressible, and a new method of treating the interface curvature is introduced for the surface tension calculations. The interface is tracked using a level set approach, with reinitialization. The algorithm is implemented in IMPACT, a multi-phase, shock physics code, with accurate representation of surface tension effects. Several validation cases have been carried out and will be presented. ^{1}R. Caiden, R. Fedkiw, & C. Anderson, J. Comput. Phys., 166, 1 (2001). |
Monday, November 19, 2018 5:10PM - 5:23PM |
L31.00006: Dissipation in adaptive wavelet Galerkin discretizations Kai Schneider, Rodrigo Pereira, Natacha Nguyen van yen, Marie Farge Adaptive wavelet schemes for solving partial differential equations offer an attractive possibility to introduce locally refined grids, which dynamically track the evolution of the solution in scale and space. Automatic error control of the adaptive discretization, with respect to a uniform grid solution, is an advantageous feature. Here we focus on dynamical Galerkin schemes, where the projection operator changes over time. When selecting a subset of basis functions, the projection operator is non-differentiable and an integral formulation has to be used. We will analyze the projected equations with respect to existence and uniqueness of the solution and prove that non-smooth projection operators introduce dissipation, a result which is crucial for adaptive discretizations of PDEs. For the Burgers equation we will illustrate numerically that thresholding the wavelet coefficients, and thus changing the projection space, will indeed introduce dissipation of energy. We discuss consequences for adaptive simulations of the incompressible Euler equations in two and three space dimensions. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L31.00007: Cascaded Lattice Boltzmann Method for Phase-Field Modeling of Incompressible Multiphase Flows Farzaneh Hajabdollahi, Kannan Premnath, Samuel Welch Two-phase fluid flows with surface tension effects are ubiquitous and challenging due to the simultaneous capturing of interfacial motion and computation of fluid motion at various scales. In this work, we have developed a cascaded lattice Boltzmann (LB) scheme using central moments and multiple relaxation times to represent the advection of an order parameter modeling the dynamics of diffuse interfaces based on a phase field model. The use of central moments improves Galilean invariance and numerical stability. In addition, to handle two-phase flows with large density contrasts in a kinetic formulation, a transformation to the distribution functions needs to be applied in the LB method that reduces the associated stiffness issues. This is accounted for by devising another new cascaded LB scheme for the fluid motion, where the central moment equilibria at different orders are reformulated in terms of the pressure field. Furthermore, the phase segregation and surface tension effects are modeled via forcing terms given in terms of changes in different central moments in this additional cascaded LB flow solver that computes the pressure and the velocity fields. Simulations of a variety of two-phase flow benchmark problems validate the new approach. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L31.00008: A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers Sk. Mashfiqur Rahman, Adil Rasheed, Omer San Numerical solution of the incompressible Navier-Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the majority of the computational cost. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the incompressible flow computations where the data-driven approach is used in solving the Poisson equation in a reduced order space. Since the time integration of the advection-diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full and reduced order spaces. We investigate the feasibility of the proposed method by solving various canonical test problems, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L31.00009: Central Moment Lattice Boltzmann Method for Computation of Flows on Stretched Lattice Grids Eman Yahia, Kannan Premnath In order to significantly expand the scope of the lattice Boltzmann (LB) method to more practical applications, particularly in the simulation of complex fluid flows with multiscale flow physics (e.g., wall-bounded flows or mixing layer flows), the use of different grid resolutions in various coordinate directions is essential. This work aims at introducing a central moments-based lattice Boltzmann (LB) scheme using multiple relaxation times (CMRT) for anisotropic meshes. The proposed model is based on a simpler and more stable natural moment basis without using orthogonality and includes additional velocity gradient terms dependent on the grid aspect ratio directly on the post-collision second order central moments to fully restore the required isotropy of the transport coefficients of the normal and shear stresses. The transformation between the distribution functions and various central moments are accomplished via shift matrices. The consistency of CMRT-LB scheme with the Navier-Stokes equations is shown via a Chapman-Enskog expansion. Numerical study for a variety of complex benchmark flow problems demonstrate its accuracy and superior numerical stability at different values of the aspect ratios of the stretched grids, when compared to other existing LB models. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L31.00010: Shock structure in viscous fluids Jason Albright, Mikhail Shashkov, Len Margolin In the context of shock-capturing numerical methods for Lagrangian gas dynamics, shock wave resolution and localization remain important practical problems. Any improvement in our understanding of 2D and 3D problems must come from a greater understanding of corresponding 1D problems. Explicit modeling of the transition profile or structure of 1D viscous shock waves goes back to the work of Becker (1921) and many others. For steady shock waves, the dependence of several shape parameters defining the structure of the smeared-transition profile, such as front location and width, have been studied previously for various forms of the viscous term including the well-known Richtmyer-von Neumann viscosity model. In this presentation, we compare several approximate shock profiles obtained using a Lagrangian, staggered-grid finite difference scheme against exact solutions of their PDE-based model counterparts using the aforementioned shape parameters to quantify the effects of different models for artificial viscosity. One objective of this comparison is to develop a structure-preserving, artificial viscosity optimization procedure that can be built into existing Arbitrary Lagrangian-Eulerian methods. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L31.00011: On the quantification of numerical dissipation and dispersion in CFD Julian Domaradzki, Giacomo Castiglioni, Guangrui Sun The method developed by Schranner et al. (2015) allows to estimate the numerical dissipation through a kinetic energy balance equation averaged over sub-domains and was applied with success to the Navier-Stokes solvers for compressible and incompressible flows. In this work we show that the method can be generalized to other PDEs and that for the linear advection equation it is in agreement with the modified equation analysis. Novelty of this work is the extension of the original method to the estimation of the dispersive error. The extension is based on a split of the residual of the kinetic energy balance equation that allows to estimate both dissipative and dispersive coefficients through a least squares method. The procedure is validated on the linear advection equation for several numerical schemes for which dispersive and dissipative errors are known. When the new method is applied to non-linear PDEs the estimates of the numerical dissipation obtained using the original method are recovered. The rigorous results obtained in this work further support the previous heuristic method for estimating numerical errors in the course of simulations performed with arbitrary Navier-Stokes solvers. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L31.00012: Accelerating direct-adjoint studies using a parallel-in-time approach |
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