Neil W. Bressloff

Optimization using surrogate models and partially converged computational fluid dynamics simulations

Efficient methods for global aerodynamic optimization using computational fluid dynamics simulations should aim to reduce both the time taken to evaluate design concepts and the number of evaluations needed for optimization. This paper investigates methods for improving such efficiency through the use of partially converged computational fluid dynamics results. These allow surrogate models to be built in a fraction of the time required for models based on converged results. The proposed optimization methodologies increase the speed of convergence to a global optimum while the computer resources expended in areas of poor designs are reduced. A strategy which combines a global approximation built using partially converged simulations with expected improvement updates of converged simulations is shown to outperform a traditional surrogate-based optimization.

Design and Analysis of "Noisy" Computer Experiments

of functions calculated by long running computer codes. The literature in this area commonly assumes that the objective function is a smooth, deterministic function of the inputs. Yet it is well known that many computer simulations,especiallythoseofcomputational fluidandstructuraldynamicscodes,oftendisplaywhatonemightcall numerical noise: rather than lying on a smooth curve, results appear to contain a random scatter about a smooth trend. This paper extends previous optimization methods based on the interpolating method ofkriging to the case of such noisy computer experiments. Firstly, we review how the kriging interpolation can be modified to filter out numerical noise. We then show how to adjust the estimate of the error in a kriging prediction so that previous approaches to optimization, such as the method of maximizing the expected improvement, continue to work effectively. We introduce the problems associated with noise and demonstrate our approach using computational fluid dynamics based problems.

Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

Kriging Hyperparameter Tuning Strategies

Response surfaces have been extensively used as a method of building effective surrogate models of high-fidelity computational simulations. Of the numerous types of response surface models, kriging is perhaps one of the most effective, due to its ability to model complicated responses through interpolation or regression of known data while providing an estimate of the error in its prediction. There is, however, little information indicating the extent to which the hyperparameters of a kriging model need to be tuned for the resulting surrogate model to be effective. The following paper addresses this issue by investigating how often and how well it is necessary to tune the hyperparameters of a kriging model as it is updated during an optimization process. To this end, an optimization benchmarking procedure is introduced and used to assess the performance of five different tuning strategies over a range of problem sizes. The results of this benchmark demonstrate the performance gains that can be associated with reducing the complexity of the hyperparameter tuning process for complicated design problems. The strategy of tuning hyperparameters only once after the initial design of experiments is shown to perform poorly.

Computational fluid dynamics modelling in cardiovascular medicine

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards ‘digital patient’ or ‘virtual physiological human’ representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations is combined with a parameterization which results in a large number of variables of seemingly equal importance. Here the authors present a variable reduction technique which employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs which result from a geometry parameterization instead of the variables which control the parameterization. The method is shown to perform well in the optimization of a two dimensional airfoil for the minimization of drag to lift ratio, producing designs better than those resulting from traditional kriging based surrogate model optimization and with a significant reduction in surrogate tuning cost

Turbulence modeling in three-dimensional stenosed arterial bifurcations.

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.

CFD PREDICTION OF COUPLED RADIATION HEAT TRANSFER AND SOOT PRODUCTION IN TURBULENT FLAMES

A novel coupled strategy is presented for predicting soot and gas species concentrations, and radiative exchange in turbulent combustion. The relatively slow processes governing soot formation are described by a model which accounts for radiative loss. In contrast to past studies, it is coupled here to the discrete transfer radiation model (DTRM) incorporating a weighted sum of gray gases (WSGG) solution to the radiative transfer equation, in an elliptic computational simulation. Incorporation of the WSGG solution in the DTRM provides a better representation of the non-gray radiative properties of combustion media than that offered by other more straightforward strategies, and without excessive computational expense. Combustion is modelled by an eddy breakup concept and the k-e turbulence model, with temperature evaluated from the solved enthalpy field. This complete strategy - the first reported of its kind - is applied to a confined turbulent jet diffusion flame burning methane in air. Confinement of the flame demands that account should be taken of the conjugate heat transfer at the boundaries. Numerical results are compared to experimental measurements of mixture fraction, temperature and soot volume fraction, and generally good agreement is achieved. Additionally, the computation of radiative exchange is considered in detail.

The development of a hybridized particle swarm for kriging hyperparameter tuning

Optimizations involving high-fidelity simulations can become prohibitively expensive when an exhaustive search is employed. To remove this expense a surrogate model is often constructed. One of the most popular techniques for the construction of such a surrogate model is that of kriging. However, the construction of a kriging model requires the optimization of a multi-model likelihood function, the cost of which can approach that of the high-fidelity simulations upon which the model is based. The article describes the development of a hybridized particle swarm algorithm which aims to reduce the cost of this likelihood optimization by drawing on an efficient adjoint of the likelihood. This hybridized tuning strategy is compared to a number of other strategies with respect to the inverse design of an airfoil as well as the optimization of an airfoil for minimum drag at a fixed lift.

Airfoil Shape Design and Optimization Using Multifidelity Analysis and Embedded Inverse Design

Design optimization using high-fidelity computational fluid dynamics simulations is becoming increasingly popular, sustaining the desire to make these methods more computationally efficient. A reduction in problem dimensions as a result of improved parameterization techniques is a common contributor to this efficiency. The focus of this paper is on the high-fidelity aerodynamic design of airfoil shapes. A multifidelity design search method is presented which uses a parameterization of the airfoil pressure distribution followed by inverse design, giving a reduction in the number of design variables used in optimization. Although an expensive analysis code is used in evaluating airfoil performance, computational cost is reduced by using a low-fidelity code in the inverse design process. This method is run side by side with a method which is considered to be a current benchmark in design optimization. The two methods are described in detail, and their relative performance is compared and discussed. The newly presented method is found to converge towards the optimum design significantly more quickly than the benchmark method, providing designs with greater performance for a given computational expense.