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

CFDNet: a deep learning-based accelerator for fluid simulations

CFD is widely used in physical system design and optimization, where it is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. However, many systems of interest are prohibitively expensive for design optimization, due to the expense of evaluating CFD simulations. To render the computation tractable, reduced-order or surrogate models are used to accelerate simulations while respecting the convergence constraints provided by the higher-fidelity solution. This paper introduces CFDNet -- a physical simulation and deep learning coupled framework, for accelerating the convergence of Reynolds Averaged Navier-Stokes simulations. CFDNet is designed to predict the primary physical properties of the fluid including velocity, pressure, and eddy viscosity using a single convolutional neural network at its core. We evaluate CFDNet on a variety of use-cases, both extrapolative and interpolative, where test geometries are observed/not-observed during training. Our results show that CFDNet meets the convergence constraints of the domain-specific physics solver while outperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows. Moreover, we demonstrate the generalization capacity of CFDNet by testing its prediction on new geometries unseen during training. In this case, the approach meets the CFD convergence criterion while still providing significant speedups over traditional domain-only models.Comment: It has been accepted and almost published in the International Conference in Supercomputing (ICS) 202

Coupling strategies for solving the RANS equations

For the present work two implicit methods of coupling the compressible Reynolds Averaged Navier-Stokes equations in conjunction with the one equation Spalart-Allmaras turbulence model have been developed. The first approach, known as fully coupled technique, strongly couples the two different systems of equations, and accordingly solves for a single system. The second technique has been defined as weakly coupled approach. On the one hand, it also solves for a single set of equations. On the other hand, the full Jacobian is not build by excluding the evaluation of the cross derivatives. The latter approach must be understood in the sense of an intermediate step between the loosely and fully coupled techniques, allowing to evaluate the coupling solution strategy. The subject of this thesis is to examine whether it is advantageous to solve the systems of equations in a mathematically consistent coupled manner or loosely coupled. For the space discretization, an unstructured finite volume scheme based on node-centered dual mesh is used. The solution procedure is based on a nonlinear agglomeration multigrid technique combined with a multistage line implicit Runge-Kutta smoother. The inner system of equations is solved through a Block Symmetric Gauss-Seidel scheme. The assessment of the newly developed methodologies is obtained by a comparative study with a loosely coupled solution strategy along with experimental data. The attention is focused on the accuracy of the results, the number of overall cycles and convergence rates of the solution method. Several numerical computations have been carried out in four two-dimensional and three-dimensional well known benchmark test cases: the CASE 9, MDA30P30N, DPW5CRM and the NASA Trap Wing. The obtained results evidence that no improvement is obtained regarding accuracy but demonstrate superiorities and inferiorities in the convergence rate for the weakly coupled and fully coupled strategies.Outgoin

CHANCE: A FRENCH-GERMAN HELICOPTER CFD-PROJECT

The paper gives an overview of the CHANCE research project (partly supported by the French DPAC and DGA and the German BMWA) which was started in 1998 between the German and French Aerospace Research Centres DLR and ONERA, the University of Stuttgart and the two National Helicopter Manufacturers, Eurocopter and Eurocopter Deutschland. The objective of the project was to develop and validate CFD tools for computing the aerodynamics of the complete helicopter, accounting for the blade elasticity by coupling with blade dynamics. The validation activity of the flow solvers was achieved through intermediate stages of increasing geometry and flow modelling complexity, starting from an isolated rotor in hover, and concluding with the time-accurate simulation of a complete helicopter configuration in forward-flight. All along the research program the updated versions of the CFD codes were systematically delivered to Industry. This approach was chosen to speed up the transfer of capabilities to industry and check early enough that the products meet the expectations for applicability in the industrial environment of Eurocopter

Implementation and Testing of Unsteady Reynolds-Averaged Navier-Stokes and Detached Eddy Simulation Using an Implicit Unstructured Multigrid Scheme

Investigation and development of the Detached Eddy Simulation (DES) technique for the computation of unsteady flows on unstructured grids are presented. The motivation of the research work is driven by the ultimate goal of predicting separated flows of aerodynamic importance, such as massive stall or flows over complex non-streamlined geometries. These cases, in which large regions of massively separated flow are present, represent a challenge for conventional Unsteady Reynolds-Averaged Navier-Stokes (URANS) models, that in many cases, cannot produce solutions accurate enough and/or fast enough for industrial design and applications. A Detached Eddy Simulation model is implemented and its performance compared to the one equation Spalart-Allmaras Reynolds-Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and URANS include decaying homogenous turbulence in a periodic domain, flow over a sphere and flow over a wing with a NACA 0012 profile, including massive stall regimes. Because of the inherent unsteadiness of turbulence, the first step towards computing separated flows is the development of an unsteady solution technique for unstructured meshes to be able to produce time accurate solutions. An implicit method for the computation of unsteady flows on unstructured grids was implemented based on an existing steady state multigrid unstructured mesh solver. The resulting non-linear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the time accurate URANS solver is performed for the well-known case of flow over a cylinder

Vorticity-transport and unstructured RANS investigation of rotor-fuselage interactions

The prediction capabilities of unstructured primitive-variable and vorticity-transport-based Navier-Stokes solvers have been compared for rotorcraft-fuselage interaction. Their accuracies have been assessed using the NASA Langley ROBIN series of experiments. Correlation of steady pressure on the isolated fuselage delineates the differences between the viscous and inviscid solvers. The influence of the individual blade passage, model supports, and viscous effects on the unsteady pressure loading has been studied. Smoke visualization from the ROBIN experiment has been used to determine the ability of the codes to predict the wake geometry. The two computational methods are observed to provide similar results within the context of their physical assumptions and simplifications in the test configuration