Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined

Adaptive design of experiments for efficient and accurate estimation of aerodynamic loads

Aerodynamic design, which aims at developing the outer shape of the aircraft while meeting several contrasting requirements, demands an accurate and reliable aerodynamic database. Computing forces and moments with the highest level of ?fidelity is a prerequisite, but practically limited by wall clock time and available computing resources. An e?fficient and robust approach is therefore sought after. This study investigates two design of experiments algorithms in combination with surrogate modelling. In traditional design of experiments, the samples are selected a priori before running the numerical explorative campaign. It is well-?known that this may result in either poor prediction capabilities or high computational costs. The second strategy employs an adaptive design of experiments algorithm. As opposed to the former, this is a self?-learning technique that iteratively: i) identi?fies the regions of the design space that are characterised by stronger non?linearities; and ii) select the new samples in order to maximise the information contentassociated with the simulations to be performed during the next iteration. In this work, the Reynolds?-averaged Navier-?Stokes equations are solved around a complete aircraft confi?guration. A representative ?flight envelope is created taking the angle of attack and Mach number as design parameters. The adaptive strategy is found to perform better than the traditional counterpart. This is quantifi?ed in terms of the sum of the squared error between the surrogate model predictions and CFD results. For the pitch moment coe?fficient, which shows strong non?linearities, the error metric using the adaptive strategy is reduced by about one order of magnitude compared to the traditional approach. Furthermore, the proposed adaptive methodology, which is employed on a high performance computing facility, requires no extra costs or complications than a traditional methodolog

Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow

Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3≤ Ma≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. Firstly, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state-of-the-art computational fluid dynamics solvers as cross-validated benchmarks. Indicial functions are calculated for a step change in the angle of attack and for a sharp-edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following an encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories

An algorithm for the regression of the UNIQUAC interaction parameters in liquid-liquid equilibrium for single- and multi-temperature experimental data

This paper describes an algorithm for the computation of the UNIQUAC interaction parameters from liquid-liquid experimental data. The algorithm comprises two separate levels. The inner level is devoted to the calculation of the interaction parameters, minimizing an objective function which is function of the activities. The outer level uses the parameters by the inner level and aims to minimize the error between experimental and calculated molar fractions through an adjustment of the experimental molar fractions, provided that the condition of common tangent to the change of the Gibbs free energy of mixing is matched. The algorithm is applied to seven binary systems for the evaluation of single temperature parameters and to the tetrahydrofuran/water system for the evaluation of the temperature dependent parameters. In both cases, the calculated parameters provide results with lower error than the previously published parameters. In all cases thermodynamically consistent and precise results are obtained in terms of common tangent of the Gibbs free energy of mixing and molar faction errors

Probing the inflationary particle content: extra spin-2 field

We study how inflationary observables associated with primordial tensor modes are affected by coupling the minimal field content with an extra spin-2 particle during inflation. We work with a model that is ghost-free at the fully non-linear level and show how the new degrees of freedom modify standard consistency relations for the tensor bispectrum. The extra interacting spin-2 field is necessarily massive and unitarity dictates its mass be in the $m \gtrsim H$ range. Despite the fact that this bound selects a decaying solution for the corresponding tensor mode, cosmological correlators still carry the imprints of such "fossil" fields. Remarkably, fossil(s) of spin $\geq 1$ generate distinctive anisotropies in observables such as the tensor power spectrum. We show how this plays out in our set-up.Comment: 25 pages, 3 figure

Parallel Computing is Everywhere

The paper deals with the OpenMP parallel implementation of a high-order Discontinuous Galerkin solver for computational fluid dynamics (CFD) and computational aeroacoustics (CAA) applications. The use of the shared memory view of the OpenMP paradigm is here explored through three different parallel implementation strategies. The numerical experiments on 2D and 3D test cases, which consider the effects of different platforms, compilers and space discretizations, indicate that all the code versions perform quite satisfactory. In particular, the OpenMP domain decomposition algorithm reaches the highest level of parallel efficiency at low computational loads, while a colouring approach excels for the largest simulations. The performance gain observed in using a hybrid MPI/OpenMP version of the DG code on large HPC facilities will be demonstrated