Karthik Duraisamy

Liszt: a domain specific language for building portable mesh-based PDE solvers

Heterogeneous computers with processors and accelerators are becoming widespread in scientific computing. However, it is difficult to program hybrid architectures and there is no commonly accepted programming model. Ideally, applications should be written in a way that is portable to many platforms, but providing this portability for general programs is a hard problem. By restricting the class of programs considered, we can make this portability feasible. We present Liszt, a domain- specific language for constructing mesh-based PDE solvers. We introduce language statements for interacting with an unstructured mesh, and storing data at its elements. Pro- gram analysis of these statements enables our compiler to expose the parallelism, locality, and synchronization of Liszt programs. Using this analysis, we generate applications for multiple platforms: a cluster, an SMP, and a GPU. This approach allows Liszt applications to perform within 12% of hand-written C++, scale to large clusters, and experience order-of-magnitude speedups on GPUs.

Large-Eddy Simulations of a Normal Shock Train in a Constant-Area Isolator

Large-eddy simulation of a normal shock train in a constant-area isolator model (M∞=1.61, Reθ≈1660) is carried out to investigate solution sensitivity with respect to a variety of physical modeling assumptions. Simulations with spanwise periodic boundary conditions are first performed, the results of which are compared with experiment and validated with a three-level grid refinement study. Due to the computational cost associated with resolving near-wall structures, the large-eddy simulation is run at a Reynolds number lower than that in the comparison experiment; thus, the confinement effect of the turbulent boundary layers is not exactly duplicated. Although this discrepancy is found to affect the location of the first normal shock, the overall structure of the shock train and its interaction with the boundary layers matches the experiment quite closely. Observations of pertinent physical phenomena in the experiment, such as a lack of reversed flow in the mean and the development of secondary shear laye...

Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

We demonstrate an adjoint based approach for accelerating Monte Carlo estimation of risk, and apply it to estimating the probability of unstart in a SCRamjet engine under uncertain conditions that are characterized by various Gaussian and non-Gaussian distributions. The adjoint equation is solved with respect to an objective function that is used to identify unstart and the adjoint solution is used to generate a linear approximation to the objective function. This linear surrogate is used to divide the uncertain input parameters into three different strata, corresponding to safe operation of the engine, uncertain operation and unstart. The probability of unstart within these strata is very different and as a result, stratified sampling significantly increases the efficiency of the risk assessment procedure by reducing the variance of the estimator. Using this technique, the Monte Carlo method was demonstrated to be accelerated by a factor of 5.4.

Assessment of transition model and CFD methodology for wind turbine flows

A detailed evaluation of the predictive capability of a Reynolds Averaged Navier Stokes (RANS) solver with a transition model is performed for wind turbine applications. The performance of the computational methodology is investigated in situations involving attached flow as well as incipient and massive flow separation and compared with experiment. Two-dimensional simulations on wind turbine airfoil sections are seen to qualitatively and quantitatively predict the onset of transition to turbulence and provide significantly improved lift and drag predictions when compared to simulations that assume fully turbulent flow. In three-dimensional wind turbine simulations, detailed validation studies of the integrated loads and sectional pressure coefficient also show definite improvements at wind speeds at which separation is incipient or confined to a small portion of the blade surface. At low wind speeds, for which the flow is mostly attached to the blade surface, and at high wind speeds, for which it is massively separated, the transition model produces similar results to a fully turbulent calculation. Overall, the performance of the transition model highlights the necessity of such models while also pointing out the need for further development.

Application of Supervised Learning to Quantify Uncertainties in Turbulence and Combustion Modeling

The accuracy of low-fidelity models of turbulent flow such as those based on the Reynolds Averaged Navier–Stokes (RANS) equations can be questionable, especially when these models are applied in situations different from those in which the models were calibrated. At present, there is no general method to quantify structural uncertainties in such models. Greater accuracy and a reliable quantification of modeling errors is much needed to expand the use of affordable simulation models in engineering design and analysis. In this paper, we introduce a methodology aimed at improving low-fidelity models of turbulence and combustion and obtaining error bounds. Towards this end, we first develop a new machine learning algorithm to construct a stochastic model of the error of low-fidelity models using information from higher-fidelity data sets. Then, by applying this error model to the lowfidelity result, we obtain better approximations of uncertain model outputs and generate confidence intervals on the prediction of simulation outputs. We apply this technique to two representative flow problems. The first application is in flamelet-based simulations to model combustion in a turbulent mixing layer; and the second application is in the prediction of the anisotropy of turbulence in a non-equilibrium boundary layer flow. We demonstrate that our methodology can be used to improve aspects of predictive modeling while offering a route towards obtaining error bounds.

Computational Analysis of Shrouded Wind Turbine Configurations

Computational analysis of di↵user-augmented turbines is performed using high resolution computations of the Reynolds Averaged Navier–Stokes equations supplemented with a transition model. Shroud geometries, generated by the extrusion of airfoil profiles into annular wings, are assessed based on their ability to capture mass-flow through the interior of the shroud. To this end, axisymmetric calculations of high-lift airfoil sections are performed. The amplification of mass flow through a shroud is found to increase nearly linearly with radial lift force, and nonlinear e↵ects are examined in terms of the location of the leading edge stagnation point. Of the shapes considered, the Selig S1223 high-lift lowRe airfoil is found to best promote mass flow rate. Following this, full three-dimensional simulations of shrouded wind turbines are performed for selected shroud geometries. The results are compared to bare turbine solutions. Augmentation ratios (defined as the ratio of the power generated by a shrouded turbine to the Betz limit) of up to 1.9 are achieved by the shrouded turbines. Peak augmentation occurs at the highest wind speed for which the flow over the bare turbine blade stays attached. Flow fields are examined in detail and the following aspects are investigated: regions with flow separation, the development of averaged velocity profiles, and the interaction between the helical turbine wake and shroud boundary layer. Finally, power augmentation is demonstrated to continue increasing at high wind velocities, at which the turbine blade would otherwise stall, if a constant tip speed ratio is maintained.

Large-Eddy and RANS Simulations of a Normal Shock Train in a Constant-Area Isolator

Large-eddy simulations (LES) of a normal shock train in a constant-area isolator (M∞ = 1.61, Reθ = 1660) are carried out with a high-order compact differencing scheme using localized artificial diffusivity (LAD) for shock capturing. We examine sensitivities of the solution to a variety of physical modeling assumptions. Simulations with spanwise periodic boundary conditions are first performed, the results of which are compared to experiment and validated with a three-level grid refinement study. Due to the computational cost associated with resolving near-wall structures, the LES is run at a Reynolds number lower than that in the comparison experiment; thus, the confinement effect of the turbulent boundary layers is not exactly duplicated. While this discrepancy affects the location of the first normal shock, the overall structure of the shock train and its interaction with the boundary layers matches the experiment quite closely. Observations of pertinent physical phenomena in the experiment such as a lack of reversed flow and the development of secondary shear layers are captured by the simulation. Next, a series of linear eddy viscosity based Reynolds Averaged Navier Stokes (RANS) simulations are performed to assess the ability of reduced-order models to accurately capture the complicated physics of multiple shock/boundary layer interactions. It is found that the RANS solutions exhibit a wide range of variations, indicating a strong sensitivity – particularly with respect to streamwise location of the initial shock -- to model formulation. Finally, three-dimensional effects due to the side walls of the isolator are investigated by performing LES of the same shock train interaction in a three-dimensional, low-aspect-ratio rectangular duct geometry. A significant three-dimensional flow feature is observed in the region of the strong initial shock, which agrees well with experimental oil flow visualizations.

Uncertainty quantification and error estimation in scramjet simulation

The numerical prediction of scramjet in-flight performance is a landmark example in which current simulation capability is overwhelmed by abundant uncertainty and error. The aim of this work is to develop a decision-making tool for balancing the available computational resources in order to equally reduce the effects of all sources of uncertainty and error below a confidence threshold. To that end, a nested uncertainty quantification and error estimation loop is proposed that balances aleatoric uncertainty, epistemic uncertainty, and numerical error in an efficient way. Application to a nozzle flow problem shows a reduction of the confidence interval by three orders of magnitude. The framework applied to the HyShot II scramjet flight experiment validation simulation indicates that the epistemic uncertainty in the RANS turbulence model is the dominating contribution to the confidence interval.

Robust Grid Adaptation for Efficient Uncertainty Quantification

the meshes to obtain more accurate solutions at each sample point in stochastic space, such a procedure can be both cumbersomeandcomputationally expensive. Toimprove theefficiencyof this process,anew robust gridadaptation technique is proposed that is aimed at minimizing the numerical error over a range of variations of the uncertain parameters of interest about a nominal state. Using this approach, it is possible to generate computational grids that are insensitive to small variations of the uncertain parameters that can both locally and globally change the solution and, as a result, the error distribution. This is in contrast with classical adjoint techniques, which seek to adapt the gridwiththeaimofminimizingnumericalerrorsforaspecific flowcondition(andgeometry).Itisdemonstratedthat flow computations on these robust grids result in low numerical errors under the expected range of variations of the uncertain input parameters. The effectiveness of this strategy is demonstrated in problems involving the Poisson equation and the Euler equations at transonic and supersonic/hypersonic speeds.

Adjoint based techniques for uncertainty quantification in turbulent flows with combustion

A discrete adjoint solver is developed for compressible uid ows involving turbulent combustion. The governing equations are the steady-state Reynolds Averaged Navier{ Stokes based transport equations for ten variables including two for turbulence and three for combustion. Turbulence is represented using the k ! model and combustion is modeled using the Flamelet Progress Variable Approach. The adjoint system of equations is determined using automatic di erentiation and solved using a robust iterative scheme. Tests are conducted on model problems involving shock-boundary layer interactions and reacting supersonic shear layers to verify adjoint-computed functional gradients and error estimates. Adjoint-based indicators are then used to aid adaptive mesh re nement targeted towards reducing error in ow solution-dependent functionals. The methodology is nally applied in a goal-oriented mesh re nement exercise in a practical three-dimensional Scramjet combustion problem. The potential of adjoint-based methods to provide error estimates and re nement indicators to optimally use computational resources to balance errors and uncertainties in complex predictive simulations is highlighted.