Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session Q10: CFD: Algorithms |
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Chair: Pavel Popov, San Diego State University Room: 137 |
Monday, November 21, 2022 1:25PM - 1:38PM |
Q10.00001: Fast Macroscopic Forcing: Exploiting locality for operator recovery Spencer H Bryngelson, Florian Schaefer, Jessie Liu, Ali Mani The macroscopic forcing method (MFM), introduced by Mani and Park (2021), is an approach for recovering lower-dimensional scaled-up operators by successively forcing a direct simulation. The MFM has already successfully recovered eddy diffusivities for RANS-like turbulence models. However, standard algorithms for MFM apply forcings to each coarse-scale degree of freedom and conduct a fine-scale simulation, which is expensive, or exploit rather strict assumptions about the coarse operator. We present an MFM algorithm that is cheaper and more general. It applies sparse reconstruction, which exposes local features in the differential operator and reconstructs the coarse one in only a few matrix-vector products. For non-local operators, we prepend this approach by peeling long-range effects with dense matrix-vector products to expose a more local operator. We demonstrate the algorithm's performance on scalar transport and channel flow problems. |
Monday, November 21, 2022 1:38PM - 1:51PM |
Q10.00002: A Bayesian Inference Approach for Inverse Transient Heat Transfer Problem Aminul Islam Khan, Prashanta Dutta, Md Muhtasim Billah, Chunhua Ying, Jin Liu Inverse transient heat transfer problems are important in many applications including process control, metallurgy, aerospace, and nuclear engineering. However, the existing techniques cannot solve inverse heat transfer problems when the unknown parameters vary with space and time. In this study, a Bayesian inference approach is developed to solve such inverse heat transfer problems. The posterior probability density function (PPDF) of unknown parameters is computed from temperature measurements in a circular steam header. The Markov chain Monte Carlo method (MCMC) is used to estimate the statistics of unknown parameters, while the Metropolis-Hastings (MH) algorithm is used to generate random samples for the posterior state space. The inverse solution is obtained by computing the expectation of the PPDF. The simulation results indicate that the estimates using MCMC-MH samples are accurate; the Bayesian approach can capture the probability distribution of the unknown local convective heat transfer coefficients and steam temperature. The stochastic Bayesian inference approach can be applied to efficiently estimate unknown boundary conditions at inaccessible locations. |
Monday, November 21, 2022 1:51PM - 2:04PM |
Q10.00003: A time-parallel Stokes solver via a new stabilized spectral finite element formulation Mahdi Esmaily A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the small vessels of the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain, strictly uses real arithmetics and permits the use of similar shape functions for pressure and velocity for ease of implementation. It involves the addition of the Laplacian of pressure to the continuity equation with a complex-valued stabilization parameter that is derived systematically from the momentum equation. The numerical experiments show the excellent accuracy and robustness of the proposed method in simulating flows in complex and canonical geometries for a wide range of conditions. The present method is mass conservative and significantly outperforms traditional techniques by lowering the cost of simulating creeping flows in complex geometries by several orders of magnitude. |
Monday, November 21, 2022 2:04PM - 2:17PM |
Q10.00004: Relaxing timestep restrictions for numerical stability in DNS Benjamin A Hyatt, Daniel Lecoanet, Evan H Anders Ensuring the numerical stability of direct numerical simulations demands a careful selection of the timestep size. When evolving flows with explicit timestepping methods, the maximum numerically stable timestep is often set by the CFL condition, which can entail high computational costs. However, in our pseudospectral simulations, we routinely observe stability when taking timesteps significantly larger than the CFL limit. In this work, we present simulations of various flows to demonstrate that they remain accurate and numerically stable outside of the CFL regime. We also leverage linear stability theory to isolate the sources of unstable growth modes in each problem. Understanding when large timesteps are viable will be beneficial to the wide class of DNS applications involving explicit timestepping, such as when solving flows with nonlinear convection. |
Monday, November 21, 2022 2:17PM - 2:30PM |
Q10.00005: A consistent finite element method for fluid flows Dongjie Jia, Mahdi Esmaily A number of finite element methods for fluid rely on streamline upwind Petrov-Galerkin stabilization term, τSUPG, that is introduced for the fine-scale approximation. The formulation for this term is conventionally dependent on the time step size, making the solution inconsistent as the time step size is changed. We propose a new definition of τSUPG that produces consistent results. This method that is implemented on top of SUPG/PSPG stabilized formulation involves replacement of time step size with a physical measure of flow acceleration relative to its velocity. Our numerical experiment shows that the conventional formulation can generate up to 50% change in the solution as the time step size is reduced, whereas the new formulation converges to a unique solution. In this presentation, we will demonstrate the characteristics of both the conventional method and our proposed method using three cases: pipe flow, 2D flow over a square, and a realistic cardiovascular flow model. |
Monday, November 21, 2022 2:30PM - 2:43PM |
Q10.00006: High-Order Semi-Lagrangian Monte Carlo Simulations of Turbulent Mixing Pavel P Popov, Hareshram Natarajan, Priyank A Dhyani, Gustaaf B Jacobs This work presents simulations of the probability density function (PDF) of species undergoing turbulent mixing. A new algorithm, the Monte Carlo semi-Lagrangian discontinuous spectral element method (DSEM-SL), is used. The algorithm is based on classic spectral element methods, with the addition of a set of samples of Lagrangian particles at each of the spectral element Gauss quadrature points. At each time step, the particles are advected with a mean velocity and a stochastic diffusion velocity; their properties are then interpolated back onto the quadrature points, where the particles are re-initialized. This provides an inherent load-balancing by keeping constant the number of particles in each element. The diffusive Wiener increment is independent between samples of particles, but the same for all particles in a sample, thus preserving the smoothness of the species’ fields. The Monte Carlo DSEM-SL code is used to simulate the PDF of species mixing in a turbulent shear layer, with velocity and length scales relevant to hydrogen micromix combustors. Verification with an existing Lagrangian PDF code is performed, and the two approaches’ computational efficiencies are compared. |
Monday, November 21, 2022 2:43PM - 2:56PM |
Q10.00007: A robust numerical framework for modeling non-isothermal phase changing multiphase flows Ramakrishnan Thirumalaisamy, Amneet Pal S Bhalla The enthalpy technique is a widely used method for modeling phase change in engineering processes, such as welding, casting, and metal additive manufacturing. These manufacturing applications are inherently multiphysics problems and involve widely varying thermo-physical properties (density, viscosity, thermal conductivity) among different phases. Nevertheless, most enthalpy formulations assume the constant density of the phase change material (PCM) and ignore its volume change effect. To model phase change problems with arbitrary large volume/density changes, we present a robust and efficient computational framework. In this framework, the level set method is combined with the enthalpy technique to simulate phase-changing solid-liquid-gas flows. A novel low Mach equation captures the volume change effect. We derive an analytical solution to the Stefan one-dimensional problem with volume change and convective effects. It's the first time this has been done. The analytical solution validates our computational model for PCMs that change density during melting/solidification. A metal casting problem exhibiting a pipe shrinkage defect is simulated to demonstrate the practical utility of our formulation. |
Monday, November 21, 2022 2:56PM - 3:09PM |
Q10.00008: Numerical stability at r=0 in cylindrical coordinates Matthew X Yao, Alexandra Baumgart, Guillaume Blanquart For physical accuracy, it is often desirable to solve the governing equations cast in the natural coordinate system of the geometry. In the case of axisymmetric flows, it is cylindrical coordinates. Although more physically realistic, the cylindrical coordinates introduce numerical challenges. The numerical stability of the convective term is characterized by the CFL condition, generally written as σ=u△t/△x<1. Near the cenerline (r=0), the CFL number in the azimuthal direction, σθ=uθ△t/r△θ, becomes highly restrictive due to the small arc length and is one to two orders of magnitude larger than the radial CFL number, σr=ur△t/△r. The goal is to relax the restriction imposed by the azimuthal CFL condition, such that only the radial CFL condition is limiting. To achieve this, we introduce a diffusion-like term, obtained through an explicit filtering of the flow variables, to remove oscillations which arise when σθ>1. The method is tested in inviscid and viscous flows and is shown to allow for larger timesteps while recovering the same solution. |
Monday, November 21, 2022 3:09PM - 3:22PM |
Q10.00009: Tailoring a vanilla finite-difference solver for high-fidelity simulations of wall turbulence at extreme scales Pedro Costa, Sergio Pirozzoli, Paolo Orlandi, Roberto Verzicco, Massimiliano Fatica, Joshua Romero Despite the leading role of Direct Numerical Simulations (DNS) in wall turbulence research, several fundamental challenges still stand. Many of these concern the flow dynamics at high Reynolds numbers that are just becoming in reach of DNS, thanks to the ever-increasing computing power and improvement of computational tools. This work focused on developing a fast and versatile numerical solver for canonical turbulent flows that can harness modern high-performance computing power while securing the fidelity of the numerical simulation. To achieve this, several changes in the algorithm, implementation, and computational setup choice have been required. Among other things, we (1) use a novel adaptive pencil domain decomposition library for distributed-memory calculations on thousands of GPUs; (2) solve the Navier-Stokes equations in a mixed-precision mode, which allowed for halving the amount of communicated data while ensuring the simulation fidelity; and (3) leveraged a physics-based natural grid and solved the equations on a moving reference frame, which greatly reduced the numerical error and computational effort. Numerical simulations of turbulent channel flow at friction Reynolds numbers of O(10 000) were performed to illustrate the fidelity and high efficiency of the resulting tool for DNS of very large systems. These improvements have been implemented in a new version of the DNS code CaNS. |
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