Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session R13: CFD: Algorithms I |
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Chair: Tony Saad, University of Utah Room: 155 C |
Monday, November 25, 2024 1:50PM - 2:03PM |
R13.00001: A coupled space-time framework aided by physics-informed neural networks to accelerate fluid flow simulations ABHISHEK BARMAN, Biswajit Khara, Baskar Ganapathysubramanian, Anupam Sharma The idea of time parallelism allows an alternate strategy to accelerate numerical simulations when it is no longer feasible to leverage the benefits of space parallelism. The strategy used in time-parallel methods essentially involves using a coarse-grid propagator/predictor method to estimate a good initial guess of the solution across the time horizon. The time domain can then be decomposed and run in parallel using the initial guess obtained using the coarse grid propagator. This approach has been discussed in several parallel-in-time (PinT) methods such as the Parareal algorithm, where a numerical solver with a very coarse time-step is used as the predictor method. |
Monday, November 25, 2024 2:03PM - 2:16PM |
R13.00002: Accelerated Neural Network Solvers of Navier Stokes Equations for Turbulent Flows Kiran Bhaganagar, David Chambers Physics-based data driven Neural Network solver is developed to solve the inertial and buoyancy-generated turbulent flows. A configurable U-Net architecture has been trained to solve the multi-scale Elliptical Partial Differential Equations. Building on the underlying concept of V-cycle multigrid methods, a Neural network framework using U-Net architecture is optimized to solve the Poisson Equation and Helmholtz equations - the characteristic form of the discretized Navier-Stokes Equations. The U-Net based Elliptical solver is coupled to the Neural network framework to accelerate the computational time measured using FLOPS by two orders of magnitude. The method is extremely promising for very high Reynolds number turbulent flows. |
Monday, November 25, 2024 2:16PM - 2:29PM |
R13.00003: Sharp, stable, and collocated numerical simulation of incompressible, multi-phase fluid flows Adam L Binswanger, Matthew Blomquist, Scott West, Shilpa Khatri, maxime theillard Motivated by atmospheric and oceanic applications, we present a novel collocated projection method for simulating incompressible multi-phase fluid flows in two and three dimensions. This method uses a modified pressure correction projection to solve the Navier-Stokes equations for the fluid flow. The fluid solver employs an adaptive mesh refinement strategy using non-graded quad/octrees and a finite volume discretization for the viscosity and projection operators. The moving interface between phases is captured using a coupled level set-reference map method, which provides a sharp representation of the interface position. This method and solver are highly adaptable to multi-physics applications. We demonstrate its capabilities through a variety of two and three dimensional density and surface tension driven multi-phase flows. We will present high fidelity simulations of single and multiple rising bubbles facing weak and strong surface deformations, as well as, fluid-solid coupling through rising bubbles flowing past solid obstructions. We additionally highlight the capability of this solver to study environmental applications by showing results of a rising oil droplet in a density stratified flow. |
Monday, November 25, 2024 2:29PM - 2:42PM |
R13.00004: Numerical stability and convergence of iterative low-Mach variable density time-integration schemes Aaron Nelson, Guillaume Blanquart Low-Mach variable-density flows are frequently encountered in turbulent reactive flows and buoyant turbulence. The stiffness of the low-Mach governing equations poses challenges for numerical stability, especially when an equation of state (EOS) relating the density and transported scalars must be satisfied. A common solution is to use an iterative time integration scheme with a pressure projection step. A computational study is performed to determine the numerical stability and convergence in two different iterative schemes: one where the EOS and scalar boundedness are satisfied but the primary conservation of the scalar is affected by iteration error, and one where the primary conservation is satisfied but the EOS and scalar boundedness are affected instead. First, the 1D governing equations are used to derive approximate analytical expressions for the convergence rates of both schemes for a binary mixture of light and heavy fluids in terms of global flow variables. This expression is confirmed in 1D direct numerical simulations (DNS). The expressions indicate lower convergence rates for the EOS-violating scheme at similar Courant-Friedrichs-Lewy (CFL) number. In 3D DNS of a turbulent planar jet of light fluid through heavy fluid, the EOS-violating case is shown to be more unstable and slower converging than the conservation-violating case, also at similar CFL. |
Monday, November 25, 2024 2:42PM - 2:55PM |
R13.00005: A Novel Add-On Tool for Calculating Hydrodynamic Force on Immersed Object Independent of Local Wall Orientation Huidan (Whitney) Yu, Matthew Blubaugh, Duan Zhong Zhang, Min Wang Hydrodynamic force (HF), resulting from drag, lift, and side forces on immersed objects, plays a critical role in automotive, aerospace, maritime, and wind engineering, as well as in sports. In computational fluid dynamics technique, HF is typically calculated from the resolved velocity gradients and pressure fields through postprocessing. However, this becomes challenging for non-flat objects due to the requirement of local wall orientation information. In this study, we derived a rigorous formulation of HF based on the Reynolds Transport Theorem equation for momentum. The HF acting on the object is calculated solely from surface integrals of velocity gradients and pressure over rectangular planes in proximity to the immersed object, eliminating the need of local wall orientation information. A systematic study has been performed to evaluate the numerical accuracy and convergence of the HF formula using the benchmark case of flow past a sphere at various Reynolds numbers. This formulation can serve as an add-on toolkit for any CFD solvers. We apply it to the volumetric lattice Boltzmann solver and verify its accuracy and convergence. Our work demonstrates that this new approach provides a robust and versatile method for calculating HF, potentially enhancing the precision of simulations in various engineering fields. |
Monday, November 25, 2024 2:55PM - 3:08PM |
R13.00006: Robust Gradient-Based Solver for Invariant Solutions to the Navier-Stokes Equations using Resolvent Analysis Thomas Burton, Davide Lasagna, Sean P Symon Low-dimensional chaotic dynamics can be modelled in terms of periodic solutions of the governing strange attractor. Analogously, exact nonlinear solutions to the Navier-Stokes equations, called Exact Coherent Structures (ECSs), are expected to serve a similar purpose for turbulence. To find these solutions, specialised numerical techniques have been devised, which largely suffer from difficulties resulting from the high dimensionality and sensitivity of the chaotic dynamics. In addition, they are rarely applied to domains that contain walls, limiting them to flows of mostly theoretical interest. In this work, the variational optimisation methodology of Schneider (2022) is extended to find periodic flows in domains that include no-slip boundary conditions. The method relies on a Galerkin projection of the “optimisation dynamics”, defined by a modal basis obtained from Resolvent Analysis (RA). RA is a technique that takes a base/mean flow and the Navier-Stokes equations as input and provides a set of response modes ranked by their receptivity to harmonic forcing of the Navier-Stokes equations. These Resolvent response modes have been shown to provide an efficient basis of ECSs for certain wall-bounded flows. This methodology is demonstrated on the Rotating Plane Couette Flow, a limiting case of the general Taylor-Couette flow, focusing on the convergence rates and accuracy of the solutions obtained. |
Monday, November 25, 2024 3:08PM - 3:21PM |
R13.00007: Fast Projection Methods for Variable Density and low-Mach Reacting Flows. Maher Eid, Tony Saad In this work, we report on the progress we made at developing a theory of fast projection methods for high-order (in time) variable density and low-Mach reacting flows. Fast-projection methods aim at eliminating the computationally expensive pressure-solve in Navier-Stokes simulations, while retaining formal accuracy and stability. These methods replace the pressure Poisson equation by rationally derived approximations for the pressure that are much cheaper to calculate than solving for the pressure itself. When compared to their conventional counterparts, where a pressure-solve is required at each stage of a high-order integrator, these methods can achieve up to 40% speedup for the same target accuracy. While the projection method has been extended to low-mach and reacting flows, fast projections methods have mainly been exclusive to incompressible flows. When applied to reacting flows, the projection method results in a variable coefficient Poisson equation for the pressure and a dilatation field that is coupled to energy, species, and scalar transport. This in turn complicates the design of fast-projection methods for low-Mach flows. In this work, we report our progress on developing a theory of fast projection methods for reacting flows and demonstrate, surprisingly, that the same pseudo-pressure approximations derived for incompressible flow case remain valid in a low- mach, reacting flow setting. |
Monday, November 25, 2024 3:21PM - 3:34PM |
R13.00008: Semi-Lagrangian Pressure Solver for Accurate, Consistent, and Conservative Volume-of-Fluid Simulations Julian Lewis Fox, Mark F Owkes Unsplit, geometric volume-of-fluid techniques are state-of-the-art numerical methods for capturing the interface between gas-liquid flows and use a semi-Lagrangian (SL) method to advect discontinuous quantities near the interface. Although highly successful, the method requires a nonphysical SL flux correction to achieve conservation of mass, momentum, and any other quantities advected with the SL discretization, which hinders the accuracy and adds computational cost. The issue arises due to an inconsistency between the SL discretization of advection terms and the finite volume discretization commonly used in the pressure equation. In this work, we propose an updated scheme that uses the SL method to consistently discretize the divergence operator in both the advection terms and the pressure equation. This ensures that the velocity field is divergence-free under a SL discretization at the next time step. This work aims to quantify gains in computational efficiency and accuracy compared to previous methods. |
Monday, November 25, 2024 3:34PM - 3:47PM |
R13.00009: Towards an adaptive mesh refinement approach for stability and resolvent Analysis of external flows around complex geometries Wei Hou, Tim Colonius We introduce an efficient and versatile numerical method to solve flow stability and resolvent analysis problems by combining the immersed boundary (IB) method, lattice Green's function (LGF), and adaptive mesh refinement (AMR). The immersed boundary method is used to represent the complex geometries without changing the underlying discretization of the PDE. The LGF ensures that we can accurately compute the stability and resolvent problems using the snuggest domain possible while maintaining the correct far-field boundary condition. Multilevel mesh is used to resolve different flow features on different length scales. Furthermore, we validated our algorithm by performing the 3D stability analysis of the flow past a rotating cylinder at various rotational rates. We also demonstrate the multilevel mesh by computing the stability problem of the flow past a cylinder with a control cylinder in its wake. Currently, we are working on leveraging the adaptive mesh refinement techniques to create tailored computational meshes to resolve the stability analysis problem for different flow configurations as accurately and as efficiently as possible. Preliminary results show that the AMR algorithm can track the vortical region of the unstable equilibrium even when it is not known a priori. |
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