Appearance concerns in later life: Do they really exist?

In Western society, where youth and beauty are given high status, older people can often feel pressured to adopt appearance-enhancing strategies, such as using anti-ageing products. Those who invest time and money into their image often do so to show they are coping well with later life and gain respect from others. Claire Hamlet examines the concept of successful ageing in relation to appearanc

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour

Turbulence Model Implementation and Verification in the SENSEI CFD Code

This paper outlines the implementation and verification of the negative Spalart-Allmaras turbulence model into the SENSEI CFD code. The SA-neg turbulence model is implemented in a flexible, object-oriented framework where additional turbulence models can be easily added. In addition to outlining the new turbulence modeling framework in SENSEI, an overview of the other general improvements to SENSEI is provided. The results for four 2D test cases are compared to results from CFL3D and FUN3D to verify that the turbulence models are implemented properly. Several differences in the results from SENSEI, CFL3D, and FUN3D are identified and are attributed to differences in the implementation and discretization order of the boundary conditions as well as the order of discretization of the turbulence model. When a solid surface is located near or intersects an inflow or outflow boundary, higher order boundary conditions should be used to limit their effect on the forces on the surface. When the turbulence equations are discretized using second order spatial accuracy, the edge of the eddy viscosity profile seems to be sharper than when a first order discretization is used. However, the discretization order of the turbulence equation does not have a significant impact on output quantities of interest, such as pressure and viscous drag, for the cases studied

Summary Data from the Sixth AIAA Computational Fluid Dynamics Drag Prediction Workshop: Code Verification

Results from the Sixth AIAA CFD Drag Prediction Workshop (DPW-VI), Case 1 Code Verification are presented. This test case is for the turbulent flow over a 2D NACA 0012 airfoil using Reynolds-Averaged Navier-Stokes (RANS) turbulence models. A numerical benchmark solution is available for the standard Spalart-Allmaras (SA) turbulence model that can be used for code verification purposes, i.e., to verify that the numerical algorithms employed are consistent and that there are no programming mistakes in the software. For the Case 1 code verification study, there were 31 data submissions from 16 teams: 23 with the SA model (using various versions), 4 with the k-omega SST model (two variants), and one each with k-kl, k-epsilon, an explicit algebraic Reynolds stress model, and the lattice Boltzmann method (LBM) with very large eddy simulation (VLES). Various grid types were employed including structured, unstructured, Cartesian, and adapted grids. The benchmark numerical solution was deemed to be the correct solution for the 21 submissions with the standard SA model, the SA-noft2 variant (without the ft2 term), and the SA-neg variant (designed to avoid nonphysical transient states in discrete settings). While many of these 21 submissions did demonstrate first-order convergence on the finer meshes, others showed either nonconvergent solutions in terms of the aerodynamic forces and moments or converged to the wrong answer. Results for this case highlight the continuing need for rigorous code verification to be conducted as a prerequisite for design, model validation, and analysis studies

Numerical Study of the Effect of Mean Three-Dimensionality on Turbulence in Adverse-Pressure-Gradient Boundary Layers

Direct numerical simulation (DNS) is used to isolate the influence of sweep on a separating turbulent boundary layer. Attention here is limited to the behavior of the turbulence within the adverse-pressure-gradient (APG) region upstream of separation. Other regions and quantities are considered in Coleman, Rumsey & Spalart. The mean three-dimensionality and outer-layer inviscid skewing have only a slight effect upon the structure of the turbulence (measured by the relationship of the components of the Reynolds-stress tensor and the efficiency of the turbulence energy transfer) compared with that of the adverse pressure gradient, which dominates both the skewed and unskewed layers

Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models

Active subspace (AS) methods are a valuable tool for understanding the relationship between the inputs and outputs of a Physics simulation. In this paper, an elegant generalization of the traditional ASM is developed to assess the co-activity of two computer models. This generalization, which we refer to as a Co-Active Subspace (C-AS) Method, allows for the joint analysis of two or more computer models allowing for thorough exploration of the alignment (or non-alignment) of the respective gradient spaces. We define co-active directions, co-sensitivity indices, and a scalar ``concordance" metric (and complementary ``discordance" pseudo-metric) and we demonstrate that these are powerful tools for understanding the behavior of a class of computer models, especially when used to supplement traditional AS analysis. Details for efficient estimation of the C-AS and an accompanying R package (github.com/knrumsey/concordance) are provided. Practical application is demonstrated through analyzing a set of simulated rate stick experiments for PBX 9501, a high explosive, offering insights into complex model dynamics