Session Q24: Computational Fluid Dynamics: General II

Effect of the Gauss-Legendre node distribution on wall turbulence in Direct Numerical Simulations of periodic channel flows using a Discontinuous Galerkin method flow solver

High-order (HO) methods in Computational Fluid Dynamics (CFD) are becoming increasingly popular. This is partly because of their higher accuracy for a given number of degrees of freedom but also due to an increased interest in the scale-resolving simulations of flows in complex geometries enabled by today’s computers. These HO methods are also particularly well suited for their implementation on Graphic Processor Units (GPU) increasing the range of flow complexity that can be solved.

HO methods are generally based on the Finite Element Method (FEM) which requires the definition of points internal to the element to achieve high orders. The choice of node distribution leads to different numerical schemes with different properties.

In this work we analyze the effect of the node distributions over the development of the boundary layer. We do this by simulations of the periodic channel flow with different distributions.

This material is based upon work supported by the Department of Energy, National Nuclear Security Administration under Award Number DE-NA0003969   

An RBF-based finite difference discretization of the Navier-Stokes equations: error analysis and applications

Radial basis function-finite differences (RBF-FD) are used to solve the incompressible Navier-Stokes equations on scattered nodes. We present a semi-implicit fractional-step method that uses a staggered grid arrangement. The RBF-QR method devised by Fornberg&Piret (2008) is used to obtain the RBF-FD weights for the spatial derivatives. We propose a rigorous error analysis strategy to identify optimal combinations of the shape parameter, Ɛ, and the stencil size, n. A modified wavenumber analysis shows that the accuracy of the RBF differentiation matrices based on the optimal parameters is comparable to 4th-order Padé-type finite differences for both first and second derivatives. The internal flow in a lid-driven cavity and a transient cylinder wake are studied as examples. The former uses quasi-uniform scattered nodes, while the latter refines the mesh near the cylinder and on the wake centerline. We demonstrate that stable solutions are obtained without the need for hyperviscosity.   

Modeling Natural Ventilation in Refugee Healthcare Shelters

Ventilation is imperative in combating airborne viruses such as SARS-CoV-2. In refugee camp healthcare shelters without mechanical ventilation systems, natural ventilation can be used to lower transmission risk. With the goal of investigating the mitigation of airborne viral concentration while also evaluating thermal comfort, we performed computational fluid dynamics (CFD) simulations to model flow, temperature, and exhaled aerosol dispersion inside a refugee camp healthcare shelter. Lacking field measurements, we used a building thermal model to solve for the CFD boundary conditions. Three recommendations can be made from the results. First, for the climate conditions considered here, ventilation should be maximized at any time of day: in the day the amount of ventilation has little impact on thermal comfort, and at night maximizing ventilation both minimizes viral concentration and improves thermal comfort. Second, window openings should be aligned with the prevailing wind direction to maximize ventilation; if the wind is 60° off-normal, ventilation rates are on average 33% less than when the wind is normal to the windows. Third, infectious patients should be placed next to leeward windows if possible, so that exhaled viral particles are drawn outside and diluted.    

Data-driven RANS Model Augmentations using Learning and Inference assisted by Feature-space Engineering

This work presents guiding principles and techniques to enable inference of robust and generalizable augmentations for RANS models from sparse experimental data in a model-consistent manner such that predictive accuracy is improved across a wide range of physical configurations (geometries/boundary conditions) without any added spurious behavior. The importance of constructing bounded features (inputs to augmentation function) via physics-based non-dimensionalization in appropriate functional forms while maintaining a balance between parsimony in the set of features and a one-to-one features-to-augmentation mapping is underlined. Particular emphasis is laid on different techniques, implementations and trade-offs associated with localized learning. The framework is tested by creating a data-driven bypass transition model which is trained on two flat plate cases and shows consistent improvements across different flat plate, turbine cascade and compressor cascade cases with varying freestream turbulence intensities, Reynolds numbers and pressure gradients.   

Parallel solution of Partial Differential Equations on Binarized Octrees

Significant savings in computer memory and computational turnaround time can be realized through adaptive mesh refinement (AMR) in fluid dynamics simulations. Tree-based implementations of the AMR technique offer many advantages, but their computer implementation can be quite involved. A binarized octree is a recent pointerless implementation of an octree that relies solely on bitwise representations of the elements of an octree where a red-black tree is then used to insert and remove elements to the octree with a guaranteed worst-case performance of O(log N). The strict adherence to the bitwise representation of an octree also enables deep levels of mesh adaptations as there is no need to convert the bitwise representation to an integer. Furthermore, neighborhood information need not be stored as it is inherent in the bitwise representation. Here, we extend a binarized octree-based AMR technique for the parallel solution of partial differential equations on distributed memory platforms. We develop non-blocking collective communication utilities for intra-processor and inter-processor information exchange and discuss various alternatives to interpolations at the coarse-fine interface. We solve the 3D Poisson equation to verify the accuracy of the overall method.   

An adaptive mesh refinement approach for high Reynolds number flows over immersed bodies

The Lattice Green's Function (LGF) has been fruitfully combined with the immersed-boundary (IB) method for efficient, scalable simulation of incompressible, external flows.   A significant source of computational savings is the snug domain enabled by only requiring grid cells in vortical flow regions and truncating them in the far wake.  However, at high Reynolds numbers, the uniform grid required by the LGF is inefficient for resolving thin boundary layers. To alleviate this constraint, we develop an adaptive mesh refinement method compatible with the LGF and IB formulations.  We perform accurate DNS of flows over immersed bodies of arbitrary shape and complexity at Reynolds numbers on the order of 10000 while reducing the number of computational cells by 99.5% compared to a non-adaptive method.  The framework is also efficient for simulating the effects of gusts on immersed bodies, particularly when they are represented as unsteady potential flows which can be imposed in our method without resolving the potential flow region.  We demonstrate both steady and gusting flows over airfoils and compare our results with companion experiments in the IIT unsteady wind tunnel.    

Data-driven approach to adaptive mesh refinement in PeleC

We study the viability of data-driven adaptive mesh refinement in PeleC, a fully compressible reacting flow solver that utilizes the AMReX library for structured mesh management. The current strategy for grid cell tagging for refinement employs ad hoc thresholding criteria on a select subset of flow variables and their gradients. We demonstrate that the neural network trained to classify cells based on a spatial discretization error threshold outperforms the existing heuristic tagging in PeleC. Various architectures including fully connected networks and convolutional neural networks are tested for efficacy and universality across regimes of a 3D turbulent CO_2 jet. Extensive testing is carried out to determine the optimal feature tensor to be input to the neural network by comparing localized flow features and global inputs such as 2D flow field slices and by employing feature importance studies.   

Second-Moment Closure Modelling of Particle Erosion in a Pipe Elbow

The erosive surface degradation in pipes, representing e.g. the process frequently encountered in coolant systems, is studied computationally. Different widely-used erosion models are preselected and implemented into an open source computational fluid dynamic code aiming at investigating their influence and quantifying their capability for predicting particle erosion. Influence of the particle-wall interaction is discussed, as well as the necessity to account for the secondary particle impact. The background turbulence model adopted is the near-wall second-moment closure model accounting for both Reynolds-stress and stress-dissipation anisotropies (Jakirlic, Maduta, 2015, IJHFF 51 and Wegt, PhD, 2021). Among a limited number of available reference databases for particle erosion process, the high Reynolds number (Re=538.000) experimental study of Solnordal et al. (2015, Wear 36-337), investigating the 90-degree pipe elbow configuration is used as a reference for the present study. Both the first oval-shaped degradation footprint resulting from the first particle impact and the triangle-shaped one representing the outcome of the second particle impact have been returned in close agreement with the experimental findings. This relates also to their overlapping region.   

Piecewise Linear Dimension Reduction as a Regularization Strategy in Data Assimilation for RANS Simulations

Data Assimilation can reduce the model-form errors of RANS simulations. A spatially distributed corrective parameter field can be introduced to the model, whose optimal values can be efficiently found by an adjoint method and a gradient-based optimization. For assimilation of experimental data, which in most cases are sparsely distributed or are based on a low-resolution grid, the inverse problem will be severely ill-posed. A regularization strategy is needed to reduce the number of local minima associated with unphysical solutions. Common regularization methods such as Tikhonov and Sobolev gradient are capable of reproducing smooth and physically reasonable internal velocity fields, however, if measurements are located close to walls and an accurate wall shear stress profile is sought, they cannot prevent over-fitting at these locations and will result in unphysical jagged profiles. We propose a new regularization strategy based on a projection of the parameter field which prevents over-fitting by constraining the parameter field into piecewise linear subdomains. We show that the method provides accurate velocity and wall shear stress profiles. In addition, it introduces no hyper-parameters and also leads to faster minimization convergence.   

Numerical solution of the three-dimensional incompressible Euler equations using the Characteristic Mapping Method

We present an efficient semi-Lagrangian Characteristic Mapping (CM) method for solving the three-dimensional incompressible Euler equations. This method evolves advected quantities by discretizing the flow map associated with the velocity field. Using the properties of the Lie group of volume preserving diffeomorphisms SDiff, long-time deformations are computed from a composition of short-time submaps which can be accurately evolved on coarse grids. This method is a fundamental extension to the CM method for two-dimensional incompressible Euler equations. We take a geometric approach in the 3D case where the vorticity is not a scalar advected quantity, but can be computed as a differential 2-form through the pullback of the initial condition by the characteristic map. This formulation is based on the Kelvin circulation theorem and gives point-wise a Lagrangian description of the vorticity field. We demonstrate through numerical experiments the validity of the method and show that energy is not dissipated through artificial viscosity and small scales of the solution are preserved. We provide error estimates and numerical convergence tests showing that the method is globally third-order accurate.