Academic Test Cases Research Articles

Coupled Discontinuous Galerkin/Finite Difference Solver on Hybrid Meshes for Computational Aeroacoustics

T HE field of direct simulation of acoustic waves propagation in the presence of a fluid in motion holds high standards of requirements. This is especially the case when it comes to industrial computational aeroacoustics (CAA), where methods must be able to copewith realistic, complex geometries while involving a high order of accuracy and yet result in affordable solvers in terms of computational resources. In that context, different computational methods have emerged over the years. Resulting from various theoretical backgrounds and approaches, they naturally hold specific characteristics, advantages, and drawbacks. Among them, discontinuous Galerkin (DG)methods [1–4] and finite difference (FD)methods [5– 7] are widely spread. The main characteristics of DG and FD methods are roughly recalled in Table 1. DGmethods arewell adapted to take into account complex geometries as they can deal with unstructured meshes [4,8]. Furthermore, their formulation naturally allows local-order refinement and is well suited for parallel computing. On the other hand, FD methods preferably run on structured meshes and are particularly efficient on Cartesian grids. They are easier to implement and less demanding in terms of CPU resources yet show good numerical dispersion and dissipation properties. Both these methods have been extensively studied, successfully implemented, and applied to that range of problems in industrial configurations. Based on this, a new family of questions have been raised. In particular, the possibility of coupling solvers of different natures in order to locally take advantage of the qualities of each method has already been studied byUtzmann et al. [9–11] in the field of CAA. We will also focus on hybridization techniques of DG/FD schemes based on a computational domain-decomposition approach. A typical motivation behind this is to be able to approximate the solution in the close neighborhood of complex obstacles on an unstructured DG mesh and compute the rest of the field on a Cartesian FD grid in order to alleviate computational time and resources. The purpose of this study is to investigate natural questions raised by such a coupling in order to gather informations on the behavior of the resulting hybrid solver in precision and stability. In this paper, we introduce two two-dimensional (2-D) DG timedomain (DGTD)/FD time-domain (FDTD) hybridization algorithms in the context of the resolution of the linearized Euler equations (LEEs) in two different kinds of geometrical configurations. Our results mainly focus on validation aspects, driven by numerical experiments that were conducted on academic test cases, as theoretical results on the interaction of these two schemes presently seem out of reach in a general case. We also present the behavior of our hybrid solver in the context of an acoustic benchmark problem that consists in the diffraction of an acoustic source by complex-geometries obstacles. The paper is organized as follows. In Sec. II, we present our physical modeling and both the FDTD andDGTD schemes that are used in this study.We also recall their compared properties, advantages, and drawbacks. In Sec. III, after presenting the numerical and theoretical issues raised by the design of a DG/FD coupled solver, we focus on our hybridization strategy and its numerical validation. In Sec. IV, we present an application of our hybrid solver to a complex-geometry acoustic test case, which was proposed at the Fourth CAA Workshop on Benchmark Problems [12].

Diffusive-Wave Based Hydrologic-Hydraulic Model with Sediment Transport. II: Validation and Practical Application

AbstractThe development of a distributed two-dimensional (2D) hydrologic-hydraulic simulation model was presented in Paper I. The simulation model combined overland flow (kinematic/diffusive wave models), hillslope sediment transport, and groundwater flow apart from the water exchange mechanisms between zones. Particular attention was paid to the upwind discretization of the surface flow equations. In this paper, the proposed model is validated by using four test cases with exact solutions, one academic test case, and two laboratory test cases. The model adequately reproduced front advance over dry beds of any slope and water table evolution in simple cases. As practical application of the model, the simulation of real events in two experimental basins is also presented. The work is focused on the influence of the choice of the empirical parameters on the model results concerning solid and liquid discharges. Also, because of the lack of information referring the boundary and initial conditions of the grou...

Tomographic reconstruction of tokamak plasma light emission from single image using wavelet-vaguelette decomposition

Images acquired by cameras installed in tokamaks are difficult to interpret because the three-dimensional structure of the plasma is flattened in a non-trivial way. Nevertheless, taking advantage of the slow variation of the fluctuations along magnetic field lines, the optical transformation may be approximated by a generalized Abel transform, for which we propose an inversion technique based on the wavelet-vaguelette decomposition. After validation of the new method using an academic test case and numerical data obtained with the Tokam 2D code, we present an application to an experimental movie obtained in the tokamak Tore Supra. A comparison with a classical regularization technique for ill-posed inverse problems, the singular value decomposition, allows us to assess the efficiency. The superiority of the wavelet-vaguelette technique is reflected in preserving local features, such as blobs and fronts, in the denoised emissivity map.

On the use of a tabulation approach to model auto-ignition during flame propagation in SI engines

The direct solving of all chemical reactions and transport phenomena responsible for the progress of combustion in internal combustion engines is today unreachable in an industrial context. Therefore, models are introduced that largely reduce the number of quantities to solve but are most often restricted to a specific combustion mode. Flame propagation and auto-ignition are two such combustion modes that interact during knocking in spark-ignition engines. The auto-ignition process may be described based on the tabulation of auto-ignition delays and reaction rates, while the flame propagation can be modelled with a coherent flame model. Because of the construction hypotheses of each model, their coupling for reactive mixtures combining both combustion modes is not straightforward. A proper treatment of the combustion progress description is necessary to avoid any bias in the individual reaction rates. The present paper proposes such a coupling approach through the definition of a specific progress variable for the auto-ignition modelling. The influence of the proper accounting for the interaction between combustion modes is demonstrated based on an academic test case and engine calculations at trace-knocking conditions.

Towards the operational estimation of a radiological plume using data assimilation after a radiological accidental atmospheric release

In the event of an accidental atmospheric release of radionuclides from a nuclear power plant, accurate real-time forecasting of the activity concentrations of radionuclides is required by the decision makers for the preparation of adequate countermeasures. The accuracy of the forecast plume is highly dependent on the source term estimation. On several academic test cases, including real data, inverse modelling and data assimilation techniques were proven to help in the assessment of the source term. In this paper, a semi-automatic method is proposed for the sequential reconstruction of the plume, by implementing a sequential data assimilation algorithm based on inverse modelling, with a care to develop realistic methods for operational risk agencies. The performance of the assimilation scheme has been assessed through the intercomparison between French and Finnish frameworks. Two dispersion models have been used: Polair3D and Silam developed in two different research centres. Different release locations, as well as different meteorological situations are tested. The existing and newly planned surveillance networks are used and realistically large multiplicative observational errors are assumed. The inverse modelling scheme accounts for strong error bias encountered with such errors. The efficiency of the data assimilation system is tested via statistical indicators. For France and Finland, the average performance of the data assimilation system is strong. However there are outlying situations where the inversion fails because of a too poor observability. In addition, in the case where the power plant responsible for the accidental release is not known, robust statistical tools are developed and tested to discriminate candidate release sites.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D–1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D–3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D–1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2 M unknowns are determined by 2 M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2 M × 2 M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden’s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden’s algorithm is identified and recommended on the basis of its computer cost and reliability.

Theoretical study and numerical simulation of textiles

We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically motivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural configuration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes. We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.

On the properness condition for modal analysis of non-symmetric second-order systems

Non-symmetric second-order systems can be found in several engineering contexts, including vibroacoustics, rotordynamics, or active control. In this paper, the notion of properness for complex modes is extended to the case of non-self-adjoint problems. The properness condition is related to the ability of a set of complex modes to represent in an exact way the behavior of a physical second-order system, meaning that the modes are the solutions of a quadratic eigenvalue problem whose matrices are those of a physical system. This property can be used to identify the damping matrices which may be difficult to obtain with mathematical modeling techniques. The first part of the paper demonstrates the properness condition for non symmetric systems in general. In the second part, the authors propose a methodology to enforce that condition in order to perform an optimal reconstruction of the “closest” physical system starting from a given basis complex modes. The last part is dedicated to numerical and experimental illustrations of the proposed methodology. A simulated academic test case is first used to investigate the numerical aspects of the method. A physical application is then considered in the context of rotordynamics. Finally, an experimental test case is presented using a structure with an active control feedback. An extension of the LSCF identification technique is also introduced to identify both left and right complex mode shapes from measured frequency response functions.

Development of a Cartesian-grid finite-volume characteristic flux model for marine applications

A Finite Volume method based on Characteristic Fluxes for compressible fluids is developed. An explicit cell-centered resolution is adopted, where second-order accuracy is provided by using a MUSCL scheme with Sweby or Superbee limiters for the hyperbolic part. Resolution is performed on a generic unstructured Cartesian grid, where solid boundaries are handled by a Cut-Cell method. Interfaces are explicitely advected in a non-diffusive way, ensuring local mass conservation of each fluid. An improved cell cutting has been developed to handle boundaries of arbitrary geometrical complexity. The mesh density is locally adapted to provide accuracy along these boundaries, which can be fixed or move inside the mesh. Instead of using a polygon clipping algorithm, we use the Voxel traversal algorithm coupled with a local floodfill scanline to intersect 2D or 3D boundary surface meshes with the fixed Cartesian grid. Small cells stability problem near the boundaries is solved using a fully conservative merging method. Inflow and outflow conditions are also implemented in the model. The solver is validated on 2D academic test cases, such as the flow past a cylinder. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the mesh. Extension to 3D is presently being implemented and first results will be presented at the conference.

Creative Entrepreneurial Applications In The Wood Industries: An Appalachian Case Study

This paper illustrates three academic units collaborative process to solve a design problem in the development of new wood products for the Historic Boone Tavern Hotel, Berea, Kentucky. The Boone Tavern Hotel chronology and renovation needs after 99 years are summarized. The Berea College Student Crafts Program is then described and the need for a new business model for designing innovative products is illustrated. The learning objectives within the academic program of the Technology and Industrial Arts Department‘s TEC 140 Class which became the ―academic test case‖ for the collaborative experiment are described. Finally an innovative model for reviewing and executing rapid prototyping within the wood products class for possible adoption by the Boone Tavern Hotel and manufactured by the Student Craft Program is revealed.

One-dimensional mathematical and numerical modeling of liquid dynamics in a horizontal capillary

This paper is concerned with a mathematical and numerical study of liquid dynamics in a horizontal capillary. We derive a two-liquids model for the prediction of capillary dynamics. This model takes into account the effects of real phenomena: like the outside flow action, or the entrapped gas inside a closed-end capillary. Moreover, the limitations of the one-dimensional model are clearly indicated. Finally, we report on several tests of interest: an academic test case that can be used to check available numerical methods, a test for decreasing values of the capillary radius, a simulation concerning a closed-end capillary, and two test cases for two liquids flow. In order to study the introduced mathematical model, our main tool, is a reliable one-step adaptive numerical approach based on a one-step one-method strategy.

Effect of multiperforated plates on the acoustic modes in combustors

The analytical model derived by Howe assessing the acoustic effect of perforated plates has been implemented in a 3D Helmholtz solver. This solver allows one to compute the acoustic modes of industrial chambers taking into account the multiperforated plates present for the cooling of the walls. An academic test case consisting of two coaxial cylinders, with the inner one being perforated is used to validate the implementation in the general purpose AVSP code. This case is also used to show the effects of the presence of the plates. In particular, the sensitivity of the acoustic damping to the bias flow speed will be studied. A maximum absorption speed is shown, and the behaviour towards an infinite speed will be illustrated by the academic case. Computations are also conducted in the case of an industrial helicopter chamber. The value of the maximum absorption speed is discussed to explain why the modes are in fact not much absorbed by the perforated plates, and that the frequencies are the same as for walls. To cite this article: E. Gullaud et al., C. R. Mecanique 337 (2009).

A Tool to Study Azimuthal Standing and Spinning Modes in Annular Combustors

A methodology for the computation of azimuthal combustion instabilities which can occur in annular combustors is proposed in this work. A thermoacoustic numerical tool using the n – τ model for the coupling of acoustic and combustion is required to solve the Helmholtz equation in reactive media. The methodology is based on the Independence Sector Assumption in Annular Combustor (ISAAC) which states that the heat release fluctuations in a given sector are driven only by the fluctuating mass flow rates due to the velocity perturbations through its own swirler. This assumption is first discussed with respect to a Large Eddy Simulation of an annular combustor. The methodology is then applied to an academic annular test case which exhibits amplified or damped, standing or rotating azimuthal eigenmodes depending on parameters n and τ.

Modeling accidental-type fluid–structure interaction problems with the SPH method

This paper presents the validation aspects of a unified numerical framework based on SPH formulation and devoted to the modeling of fluid–structure interaction problems involving large motion of the fluid and large deformation with a possible failure of the structure. The fluid domain is modeled according to an updated Lagrangian formulation. The solid domain (3D and shell models) uses the total Lagrangian formulation. The fluid–structure interaction is treated via a unilateral contact algorithm adapted to SPH context. The SPH framework is verified on academic test cases and validated by simulating an experiment involving the reservoir leakage.

A mapping method based on Gaussian quadrature: Application to viscous mixing

In this work, a novel mapping method based on distributed Gaussian quadrature is proposed to analyze viscous distributive mixing criteria when considering geometry and/or time periodic laminar flows. It avoids the recourse to the mesh tracking procedure that is hard to manage. In addition, its extension to 3D is straightforward. The appeal of the mapping technique is that it is independent from initial feeding conditions of the passive phase (e.g. pigments or additives). The mapping matrix is calculated once over a single hydrodynamic period. Then, successive mixing patterns are recovered by multiplying, as much as needed, the mapping matrix by the chosen feeding conditions. The behavior of this new method is verified on academic test cases to determine its accuracy. It is found that by increasing the number of Gauss points per element, the accuracy of predicted concentration patterns improves. Finally, the new mapping method is applied on twin-screw extruders and a Kenics static mixer. The predicted concentration patterns are found to be in good agreement in regards to available experimental and computational data. Also, it is found that improved spatial discretization helps to recover high accuracy mixing patterns resulting from repeated mapping steps.

Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and “low-cost” shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine.

Eikonal equation‐based front propagation for arbitrary complex configurations

AbstractThis paper presents a front propagation method using the Eikonal equation, ∇ϕ ⋅ ∇ϕ = 1, in which, ϕ represents the smallest Euclidean distance field to the front to be propagated. The offset capturing approach consists in first calculating the ϕ field over a uniform Cartesian grid fully covering the front to be propagated, and then constructing the iso‐ϕ curves or surfaces as the propagated result. The calculation of ϕ uses a 3D numerical scheme, the Fast Sweeping Scheme. Validation for accuracy of the method is presented using academic test cases. A real 3D industry application, draft tube with two piers, is successfully propagated and demonstrated using special boundary conditions to cope with inlet and outlet planes during front propagtion. This application involves the propagation of a front that exhibits both concave and convex shape regions, sharp corners, and local tangent plane surface discontinuities as well as a multi‐connected domain. Copyright © 2007 John Wiley & Sons, Ltd.

ISAC: Integrated Space-and-Time-Adaptive Chip-Package Thermal Analysis

Ever-increasing integrated circuit (IC) power densities and peak temperatures threaten reliability, performance, and economical cooling. To address these challenges, thermal analysis must be embedded within IC synthesis. However, this requires accurate three-dimensional chip-package heat flow analysis. This has typically been based on numerical methods that are too computationally intensive for numerous repeated applications during synthesis or design. Thermal analysis techniques must be both accurate and fast for use in IC synthesis. This paper presents a novel accurate incremental spatially and temporally adaptive chip-package thermal analysis technique called ISAC for use in IC synthesis and design. It is common for IC temperature variation to strongly depend on position and time. ISAC dynamically adapts spatial- and temporal-modeling granularities to achieve high efficiency while maintaining accuracy. Both steady-state and dynamic thermal analyses are accelerated by the proposed heterogeneous spatial-resolution adaptation and asynchronous thermal-element time-marching techniques. Each technique enables orders-of-magnitude improvement in performance while preserving accuracy when compared with other state-of-the-art adaptive steady-state and dynamic IC thermal analysis techniques. Experimental results indicate that these improvements are sufficient to make accurate dynamic and steady-state thermal analysis practical within the inner loops of IC synthesis algorithms. ISAC has been validated against reliable commercial thermal analysis tools using industrial and academic synthesis test cases and chip designs. It has been implemented as a software package suitable for integration in IC synthesis and design flows and has been publicly released

Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.

Numerical simulations of gas-particle flows with combustion

This work is devoted to the numerical modelling of a reactive gas-particle flow that arises in internal ballistic. The model, proposed by Gough [2], takes into account complex physical phenomena such as mass transfer, drag force or intra granular stress. A non-conservative finite volume approach adapted from [11] is applied in order to simulate the model. After an academic validation test case of the scheme, the combustion propagation ignited by a cylindrical perforated primer is then simulated and compared with experiments.