Academic Test Cases Research Articles

Topological data assimilation using Wasserstein distance

This work combines a level-set approach and the optimal transport-based Wasserstein distance in a data assimilation framework. The primary motivation of this work is to reduce assimilation artifacts resulting from the position and observation error in the tracking and forecast of pollutants present on the surface of oceans or lakes. Both errors lead to spurious effect on the forecast that need to be corrected. In general, the geometric contour of such pollution can be retrieved from observation while more detailed characteristics such as concentration remain unknown. Herein, level sets are tools of choice to model such contours and the dynamical evolution of their topology structures. They are compared with contours extracted from observation using the Wasserstein distance. This allows to better capture position mismatches between both sources compared with the more classical Euclidean distance. Finally, the viability of this approach is demonstrated through academic test cases and its numerical performance is discussed.

Modelling the damping at the junction between two substructures by non-linear meta-models

We are interested in the modelling of the damping at the level of the junction between two substructures. We model the connection by a meta-model which takes into account both dissipative and non-linear aspects of the connection. We use the Bouc-Wen meta-model. This model is adapted to be able to be inserted into a finite elements model. We obtained a non-linear dynamical system, which can be solved in the time domain with a Runge-Kutta algorithm. A software tool corresponding to this method is developed. To decrease calculation costs, we reduce the size of the system by a Craig-Bampton method. We present an application on an academic test-case, and also a comparison with experimental results.

Low order modeling method for assessing the temperature of multi-perforated plates

A low-order model is proposed to predict the temperature of a multi-perforated plate from an unresolved adiabatic computation. Its development relies on the analysis of both an adiabatic and a conjugate heat transfer wall resolved large eddy simulation of an academic multi-perforated liner representative of the cooling systems used in combustion chambers of actual aero-engines. These two simulations show that the time averaged velocity field is marginally modified by the coupling with the heat diffusion in the perforated plate when compared to the adiabatic case. This gives rise to a methodology to assess the wall temperature from an unresolved adiabatic computation. It relies on heat transfer coefficients from referenced correlations as well as a mixing temperature relevant to the flow in the injection region where the cold micro-jets mix with the hot outer flow. In this approach, a coarse mesh simulation using an homogeneous adiabatic model for the aerodynamics of the flow with effusion is post-processed to provide a low cost alternative to conjugate heat transfer computations based on hole resolved meshes. The model is validated on an academic test case and successfully applied to a real industrial combustion chamber.

Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty

This paper aims at presenting sensitivity estimators of a rare event probability in the context of uncertain distribution parameters (which are often not known precisely or poorly estimated due to limited data). Since the distribution parameters are also affected by uncertainties, a possible solution consists in considering a second probabilistic uncertainty level. Then, by propagating this bi-level uncertainty, the failure probability becomes a random variable and one can use the mean estimator of the distribution of the failure probabilities (i.e. the “predictive failure probability”, PFP) as a new measure of safety. In this paper, the use of an augmented framework (composed of both basic variables and their probability distribution parameters) coupled with an Adaptive Importance Sampling strategy is proposed to get an efficient estimation strategy of the PFP. Consequently, double-loop procedure is avoided and the computational cost is decreased. Thus, sensitivity estimators of the PFP are derived with respect to some deterministic hyper-parameters parametrizing a priori modeling choice. Two cases are treated: either the uncertain distribution parameters follow an unbounded probability law, or a bounded one. The method efficiency is assessed on two different academic test-cases and a real space system computer code (launch vehicle stage fallback zone estimation).

Modeling of Mineral Dust Emissions with a Weibull Wind Speed Distribution Including Subgrid-Scale Orography Variance

AbstractThe modeling of mineral dust emissions requires an extensive knowledge of the wind speed close to the surface. In regional and global models, Weibull distributions are often used to better represent the subgrid-scale variability of the wind speed. This distribution mainly depends on akparameter, itself currently parameterized as a function of the wind speed value. In this study we propose to add the potential impact of the orography variance in the wind speed distribution by changing thekparameter value. Academic test cases are designed to estimate the parameters of the scheme. A realistic test case is performed over a large domain encompassing the northern part of Africa and Europe and for the period 1 January–1 May 2012. The results of the simulations are compared to particulate matter (PM10) surface concentrations and Aerosol Robotic Network (AERONET) aerosol optical depth and aerosol size distribution. We show that with the orography variance, the simulation results are closer to the ones without variance, showing that this additional variability is not the main driver of possible errors in mineral dust modeling.

Model comparison of two different non-hydrostatic formulations for the Navier-Stokes equations simulating wind flow in complex terrain

An anelastic model and a quasi-compressible model for the simulation of wind flow in complex terrain are presented. The models are based on the Reynolds Averaged Navier-Stokes (RANS) equations in combination with the k-ε turbulence model. Additional terms are implemented in the transport equations to describe stratification of the atmosphere to account for the Coriolis forces driven by the Earth's rotation, as well as for the drag-forces and turbulence production and dissipation due to different types of land use.The modelling approaches are verified by means of academic test cases assessing effects of the Earth's rotation, density driven flow and canopy. The validation of the models is performed by investigating a wind test site near Geislingen a. d. Steige in Southern Germany. Fife hole probe velocity measurements using MASC systems (unmanned small research aircraft UAV) at different locations are compared with the simulation results for the main wind regime. Therefore, the orography and flora of the Earth's surface are described by high-resolution digital data from State Authorities for Spatial Information and Rural Development Baden-Württemberg (LGL). Boundary and initial conditions are based on mesoscale simulation data from the COSMO-DE weather model of the German Meteorological Service (DWD).

Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment

This paper aims at comparing two different approaches to perform a reliability analysis in a context of uncertainties affecting probability distribution parameters. The first approach called “nested reliability approach” (NRA) is a classical double-loop-approach involving a sampling phase of the parameters and then a reliability analysis for each sampled parameter value. A second approach, called “augmented reliability approach” (ARA), requires to sample both distribution parameters and basic random variables conditional to them at the same phase and then integrate simultaneously over both domains. In this article, a numerical comparison is led. Possibilities offered by both approaches are investigated and the advantages of the ARA are illustrated through the application on two academic test-cases illustrating several numerical difficulties (low failure probability, nonlinearity of the limit-state function, correlation between input basic variables) and two real space system characterization (a launch vehicle stage fallback zone estimation and a collision probability between a space debris and a satellite estimation) for which only the ARA is tractable.

An efficient FSI coupling strategy between Smoothed Particle Hydrodynamics and Finite Element methods

An efficient coupling between Smoothed Particle Hydrodynamics (SPH) and Finite Element (FE) methods dedicated to violent fluid–structure interaction (FSI) modeling is proposed in this study. The use of a Lagrangian meshless method for the fluid reduces the complexity of fluid–structure interface handling, especially in presence of complex free surface flows. The paper details the discrete SPH equations and the FSI coupling strategy adopted. Both convergence and robustness of the SPH-FE coupling are performed and discussed. More particularly, the loss and gain in stability is studied according to various coupling parameters, and different coupling algorithms are considered. Investigations are performed on 2D academic and experimental test cases in the order of increasing complexity.

On the dual Craig–Bampton method for the forced response of structures with contact interfaces

Assembled structures are characterized by contact interfaces that introduce a local non-linearity and affect the dynamics of the assembly in terms of resonance frequencies and vibration levels. To assess the forced response levels of the assemblies during the design, nonlinear dynamic analyses are performed and, in order to reduce the computation time, spatial and temporal reductions of the governing equations must be used. A classical way to achieve temporal reduction is to implement the harmonic balance method to turn the time-domain differential governing equations into frequency-domain algebraic equations. Due to the local nature of contact interfaces, which usually involve a subset of degrees of freedom (dofs) of the structure, a common strategy to achieve spatial reduction is to use component mode synthesis (CMS), by retaining the contact dofs as master dofs. In this paper, a recent CMS approach, named dual Craig–Bampton method (Rixen in J Comput Appl Math, 2004. doi: 10.1016/j.cam.2003.12.014 ), is applied to the nonlinear forced response of structures with contact interfaces. The spectral orthogonality of the two subsets of mode shapes used as a projection basis is exploited to write a set of algebraic equations of the contact dofs in the frequency domain, with no need to compute the reduced matrices of the system. Different formulations of the governing equations are proposed for different configurations (i.e., outer contacts, inner contacts and structures with floating components), and two academic numerical test cases are used to demonstrate the method.

Reconstruction and separation of vibratory field using structural holography

A method for reconstructing and separating vibratory field on a plate-like structure is presented. The method, called “Structural Holography” is derived from classical Near-field Acoustic Holography (NAH) but in the vibratory domain. In this case, the plate displacement is measured on one-dimensional lines (the holograms) and used to reconstruct the entire two-dimensional displacement field. As a consequence, remote measurements on non directly accessible zones are possible with Structural Holography. Moreover, as it is based on the decomposition of the field into forth and back waves, Structural Holography permits to separate forces in the case of multi-sources excitation. The theoretical background of the Structural Holography method is described first. Then, to illustrate the process and the possibilities of Structural Holography, the academic test case of an infinite plate excited by few point forces is presented. With the principle of vibratory field separation, the displacement fields produced by each point force separately is reconstructed. However, the displacement field is not always meaningful and some additional treatments are mandatory to localize the position of point forces for example. From the simple example of an infinite plate, a post-processing based on the reconstruction of the structural intensity field is thus proposed. Finally, Structural Holography is generalized to finite plates and applied to real experimental measurements

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

A multi-scale analysis of drug transport and response for a multi-phase tumour model

In this article, we consider the spatial homogenisation of a multi-phase model for avascular tumour growth and response to chemotherapeutic treatment. The key contribution of this work is the derivation of a system of homogenised partial differential equations describing macroscopic tumour growth, coupled to transport of drug and nutrient, that explicitly incorporates details of the structure and dynamics of the tumour at the microscale. In order to derive these equations, we employ an asymptotic homogenisation of a microscopic description under the assumption of strong interphase drag, periodic microstructure, and strong separation of scales. The resulting macroscale model comprises a Darcy flow coupled to a system of reaction–advection partial differential equations. The coupled growth, response, and transport dynamics on the tissue scale are investigated via numerical experiments for simple academic test cases of microstructural information and tissue geometry, in which we observe drug- and nutrient-regulated growth and response consistent with the anticipated dynamics of the macroscale system.

Parabolized Stability Equations Code with Automatic Inflow for Swept Wing Transition Analysis

This paper aims at developing a parabolized stability equation transition analysis code coupled to the industrial in-house accurate Reynolds-averaged Navier–Stokes code developed at Israel Aerospace Industries for stability analysis of three-dimensional boundary layers over swept wings. In the first step, the parabolized stability equation derivation in a body-fitted coordinate system is exposed, as well as its classical initialization, using the solution procedure of the global Chebyshev eigenvalue problem for the linear stability equations. This initialization procedure demands large user interactions, and it prevents the parabolized stability equation method to be of practical use in an industrial environment. Therefore, one exposes in the second step a new way to automatically generate the inflow solution of the linear stability equations needed by the parabolized stability equations. This new robust approach paves the way for innovative automatic industrial use of the parabolized stability equation technology without the need to involve the user. This approach supplies the inflow conditions required for the parabolized stability equation marching procedure without the need to solve the standalone linear stability global eigenvalue problem. The solution of the linear stability equations at initialization is now obtained by iteratively converging the local linear stability solver starting from the new inflow empirical approximation obtained in two special coordinate systems for crossflow and Tollmien–Schlichting, respectively. These formulas represent some invariant functions of the stability characteristics of the exact Navier–Stokes laminar boundary-layer profiles instead of self-similar boundary-layer profiles like the Falkner–Skan–Cooke. Standard academic validation test cases and industrial results of the parabolized stability equation/Reynolds-average Navier-Stokes codes on a generic unmanned aerial vehicle swept wing are exposed.

Fast frequency sweep method for indirect boundary element models arising in acoustics

This paper presents an efficient approach for computing frequency sweeps with fine increments of acoustic systems described by the variational indirect boundary element method. The matrices arising from such boundary element discretizations are fully populated and their assembly is computationally demanding as it involves the calculation of double surface integrals for each system matrix entry. Therefore, the two operations performed when computing the response at one frequency, namely assembling the system matrix and solving the associated linear system, may be of the same order of magnitude in terms of the required computational time. The proposed fast frequency sweep approach accelerates both operations. First, it avoids forming the system matrices for each individual frequency. Matrices are only assembled at a few master frequencies, while for the rest, interpolation is used on scaled quantities determined at the master frequencies. Second, it avoids solving a dense linear system at each frequency. Padé approximants constructed via the well-conditioned asymptotic waveform evaluation algorithm are used to extrapolate the response around expansion frequencies using derivative information. The proposed method was tested on an exterior acoustics application representing an academic test case, as well as on an interior/exterior application representing an industrial test case.

Modeling the Effect of Waves on the Diurnal Temperature Stratification of a Shallow Lake

In this paper a three-dimensional circulation model has been applied to determine the spatial distribution of the temperature and mixed-layer depth (MLD) of a medium-sized shallow lake. In order to reproduce the vertical thermal structure of the lake, the impact of waves has been incorporated using several recently published schemes. These schemes approximate the additional mixing due to the orbital motion of waves, the turbulent kinetic energy produced by waves, or both. The reference solver is the Reynolds-Averaged Navier-Stokes equations with two-equation Mellor-Yamada 2.5 turbulence closure. The wave field is characterized by bulk parameters, e.g. significant wave height. The sensitivity to the choice of the wave mixing scheme is analyzed by means of an academic test case. The accuracy of the scheme is explored through data collected in Lake Balaton. The modeled temperature profiles and MLDs match measurements much better when the effect of non-breaking surface waves is included.

Unified Hydrological Flow Routing for Variational Data Assimilation and Model Predictive Control

Hydrological flow routing covers a class of simple and computationally highly efficient techniques for steep river reaches without backwater effects. It is often applied as a routing component in semi-distributed and distributed hydrological models or as a stand-alone routing scheme in flow forecasting systems. If embedded into variational data assimilation (DA) or model predictive control (MPC), i.e. running the model in optimization mode, three main characteristics of the routing approach become essential: i) numerical robustness, ii) mass conservation and iii) the efficient computation of first-order sensitivities.We present a unified approach in which we reformulate various hydrological routing approaches as a cascade of non-linear reservoirs. This covers linear and nonlinear reservoir routing as well as Muskingum-type schemes. Whereas original variable-parameter versions of these schemes, e.g. Muskingum-Cunge, are not mass conservative, the reformulated version guarantees strict mass conservation. An iterative Newton-Raphson scheme integrates the implicit schematization of the reservoir equation in time. The first order sensitivities are derived by the implicit function theorem and the adjoint sensitivity equation at the computational costs of the time integration itself.The novel framework is applied to an academic test case and a routing network in the upper basin of Main River in Germany. Results show the performance of the routing scheme and verify the mass conservation properties of the approach. Furthermore, we give an outlook at the future use of the model within variational DA and MPC scenarios.

A semi-implicit immersed boundary method and its application to viscous mixing

Computational fluid dynamics (CFD) simulations in the context of single-phase mixing remain challenging notably due the presence of a complex rotating geometry within the domain. In this work, we develop a parallel semi-implicit immersed boundary method based on Open∇FOAM, which is applicable to unstructured meshes. This method is first verified on academic test cases before it is applied to single phase mixing. It is then applied to baffled and unbaffled stirred tanks equipped with a pitched blade impeller. The results obtained are compared to experimental data and those predicted with the single rotating frame and sliding mesh techniques. The proposed method is found to be of comparable accuracy in predicting the flow patterns and the torque values while being straightforwardly applicable to complex systems with multiples impellers for which the swept volumes overlap.

Coupling 3-D Navier Stokes and 1-D Shallow Water

The present work addresses the problem of coupling hydrodynamical models with different spatial dimensions, which can be used in order to reduce the computational cost of river numerical models. We show that this problem can be tackled quite efficiently by designing a simple algorithm using techniques borrowed from domain decomposition theory. This algorithm is non intrusive, i.e. allows using existing numerical models with very few modifications. The method is illustrated on an academic test-case, namely a free surface flow in a bend-shaped channel. A 3-D Navier-Stokes model is coupled with a 1-D shallow water model, and results are compared to those obtained in a fully 3-D case. It is shown that the coupling algorithm provides an accurate solution, which can be improved thanks to an iterative algorithm (Schwarz method). This study is performed using the Mascaret-Telemac system.

Time consistent fluid structure interaction on collocated grids for incompressible flow

Abstract Consistent time integration on collocated grids for incompressible flow has been studied for static grids using the PISO method, in which the dependencies on time-step size and under-relaxation has been studied in detail. However, for moving grids a detailed description is still missing. Therefore, a step by step analysis of a time consistent fluid–structure interaction (FSI) method for incompressible flow on collocated grids is presented. The method consist of: face normal and area correction for moving grids, treatment of velocity boundary conditions for no-slip walls, time integration of structure equations and fluid force interpolation to structure. The basis of the method is the PISO method of the incompressible Navier–Stokes equations. Time consistency on static grids is shown first, after which time consistency on moving grids is described and analyzed. For moving grids consistent time integration is described in two ways: (1) constructing the face velocities from a normal and tangential component, and (2) correcting the face flux with a face normal and face area correction. For both descriptions the general formulation for the backward differencing schemes (BDF) are given and the correct behavior of the first, second and third order schemes is demonstrated by means of an academic test case (circular cavity flow). Additionally, the (force) coupling from the fluid to the structure is discussed in detail for combining a fourth order explicit Runge Kutta scheme for the structure with a BDF scheme for the fluid. Three interpolations for the fluid forces are shown, which result in either a first order or second order FSI scheme. Third order FSI is demonstrated when the third order BDF scheme is applied on both the structure and fluid equations. Also, under-relaxation for the fluid equations is considered and it is demonstrated that the order of the three BDF schemes are independent of the under-relaxation factor. Finally, the proposed method of time consistent FSI on collocated grids for incompressible flows is demonstrated by applying it to a three-dimensional flow over an elastic structure in a channel and the cylinder flap FSI benchmark case of Turek and Hron.

Well-posed initial conditions and numerical methods for one-dimensional models of liquid dynamics in a horizontal capillary

In this paper, we undertake a mathematical and numerical study of liquid dynamics models in a horizontal capillary. In particular, we prove that the classical model is ill-posed at initial time, and we recall two different approaches in order to define a well-posed problem. Moreover, for an academic test case, we compare the numerical approximations, obtained by an adaptive initial value problem solver based on an one-step one-method approach, with new asymptotic solutions. This is a possible way to validate the adaptive numerical approach for its application to real liquids.