Documents published in Scipedia

• A fully-discrete entropy conserving/stable discretization for inviscid unsteady flows

  A. Colombo, A. Crivellini, A. Nigro

  eccomas2022.

  
  

  Abstract

  The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To do this, the general framework is based on a high-order accurate discontinuous Galerkin (dG) method in space with entropy working variables, several entropy conservative and stable numerical fluxes and an entropy conserving modified Crank-Nicolson method. We present the first results, obtained with the discretizations here proposed, for two bi-dimensional unsteady viscous test-case: the Taylor-Green vortex and the double shear layer.

  Abstract
  The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To [...]

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• Influence of the turbulent wake downstream offshore wind turbines on larval dispersal: development of a new Lagrangian-Eulerian model

  S. Ajmi, M. Boutet, A. Bennis, J. Dauvin

  eccomas2022.

  
  

  Abstract

  In the context of future offshore wind farms along the French coasts of the English Channel, the impacts of foundations on larval dispersal from bentho-pelagic species colonizing the hard substratum of artificial structures are studied in order to assess how the species connectivity could be modified by the farms. In particular, the effects of turbulent wake and horseshoe vortices are investigated. To this end, a new numerical approach is developed that combines the Eulerian model, OpenFoam, solving the 3D Navier-Stokes equations to compute the hydrodynamics, and the Lagrangian model, Ichthyop, based on an advection-diffusion equation to compute the larval trajectories. Firstly, some simple test cases are performed to validate the numerical coupling between OpenFoam and Ichthyop, such as the dispersion of larvae downstream a 2D cylinder in water. Secondly, the ability of OpenFoam turbulence models to simulate turbulent structures around monopile and gravity type foundations is evaluated. The RANS (Reynolds Averaged Navier-Stokes) k-omega SST turbulence model is chosen for the realistic application because it can reproduce the horseshoe vortices and turbulent wake with less computing time than the Smagorinsky LES (Large Eddy Simulation) model. Lastly, larval dispersal simulations for four benthic species and for a set of monopile and gravity foundations are performed.

  Abstract
  In the context of future offshore wind farms along the French coasts of the English Channel, the impacts of foundations on larval dispersal from bentho-pelagic species colonizing [...]

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• Surrogate modeling of unsteady aerodynamic loads acting on a plunging airfoil

  R. Sundar, V. KUMAR, D. Majumdar, C. Shah, S. Sarkar

  eccomas2022.

  
  

  Abstract

  Cost-effective parameteric surrogate models of unsteady aerodynamic loads acting on a flapping wing are highly desirable. They would enable real time aerodynamic load prediction, multiobjective optimisation and optimal control of intelligent flapping wing flight devices. In the present work, a parametric surrogate modeling framework for unsteady aerodynamic loads based on a non-intrusive reduced order modeling approach is presented. The unsteady flow past a plunging 2D flat plate is considered where the aerodynamic load time histories are obtained for different plunging frequencies and amplitudes using a potential flow solver. The parametric non-intrusive reduced order model (p-NIROM) for the obtained loads is constructed using a combination of snapshot proper orthogonal decomposition (POD) for dimensionality reduction and a fully connected feed forward neural network (FCNN) for modeling the input parametric dependency. Both, linear and non-linear FCNN based p-NIROM are explored and compared on the basis of load time history reconstruction accuracy. The non-linear FCNN regression for the p-NIROM is observed to generalise well for unseen parametric instances as compared to the linear approach when a systematic data sampling strategy is adopted.

  Abstract
  Cost-effective parameteric surrogate models of unsteady aerodynamic loads acting on a flapping wing are highly desirable. They would enable real time aerodynamic load prediction, [...]

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• Linear and quadratic invariants preserving discretization of Euler equations

  G. Coppola, A. Veldman

  eccomas2022.

  
  

  Abstract

  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid on uniform and non-uniform (Cartesian) meshes, have been recently derived by using a matrix-vector approach, for both finite-difference and finite-volume methods ([1, 2]). In this work, which constitutes a follow-up investigation of the analysis presented in [1, 2], this theory is applied to the spatial discretization of convective terms for the system of Euler equations. A classical formulation already presented in the literature is investigated and reformulated within the matrix-vector approach. The relations among the discrete versions of the various terms in the Euler equations are analyzed and the additional degrees of freedom identified by the proposed theory are investigated. Numerical simulations on a classical test case are used to validate the theory and to assess the effectiveness of the various formulations.

  Abstract
  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid [...]

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• Validation on a new anisotropic four-parameter turbulence model for low Prandtl number fluids

  L. Sirotti, G. Barbi, A. Chierici, V. Giovacchini, S. Manservisi

  eccomas2022.

  
  

  Abstract

  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the gradient-diffusion hypothesis and Reynolds analogy are inadequate to simulate the turbulent heat transfer in low-Prandtl number fluids. Additional transport equations for thermal variables are required to predict the characteristic thermal time scale. In a four-parameter turbulence model, two additional transport equations are solved for the temperature variance and its dissipation rate. Thus, it is possible to formulate appropriate characteristic time scales to predict the near-wall and bulk behaviour of mean and turbulent variables. The isotropic version of the four-parameter model has been widely studied and validated in forced and mixed convection. We aim to extend the model validity by proposing explicit algebraic models for the closure of Reynolds stress tensor and turbulent heat flux. For the validation of the anisotropic four-parameter turbulence model, low-Prandtl number fluids are simulated in several flow configurations considering buoyancy effects and numerical results are compared with DNS data.

  Abstract
  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the [...]

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• Numerical Testcases to Study Proudman Resonance Using Shallow Water Models

  N. Beisiegel, J. Behrens

  eccomas2022.

  
  

  Abstract

  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with respect to represent mentioned resonance. With the test cases we assess the wave amplification in dependence of characteristics of the pressure perturbation, model parameters, model resolution, and bathymetry characteristics. We use the compilation of tests to validate an adaptive discontinuous Galerkin (DG) model for the two-dimensional non-linear shallow water equations. As the tests are highly sensitive to model resolution, we use the adaptive mesh capabilities of the model to locally refine the disturbance and thus gain considerable efficiency.

  Abstract
  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with [...]

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• Correcting the discretization error of coarse grid CFD simulations with machine learning

  A. Kiener, S. Langer, P. Bekemeyer

  eccomas2022.

  
  

  Abstract

  Computational fluid dynamics is a cornerstone for the modern aerospace industry, providing important insights on aerodynamic analysis while reducing the need of expensive experiments and tests. Nevertheless, simulations of complex geometries are often performed on a discrete spatial domain too coarse to capture all relevant physical phenomena for the sake of lowering the computational cost. A consistent spatial discretization on so-called grids approximates the analytical solution of the partial differential equation with increasing number of discrete points. Such a grid refinement study is an expensive method to assess the general grid quality. This work shows that machine learning as a post-processing tool is capable of improving coarse grid simulations, even if not converged. The results show that three machine learning models varying in their complexity, namely the random forest, the neural network, and the graph neural network, are capable of finding patterns in coarse grid simulations. These patterns are used to predict the discretization error to approximate the field variables of interest of the corresponding fine grid simulation mapped onto the coarse grid. Initial training and testing is performed on the RAE2822 airfoil leading to corrected flow fields, improved surface integrals and coefficients, even when shocks are present. Additional tests are performed on the RAE5212 airfoil, showing the generalization limits of the trained models. The proposed method promises to reduce computational expenses while increasing the accuracy of the coarse grid results which works locally, e.g. it corrects the error for each cell individually and is therefore not restricted by the number of grid points. The presented results obtained by the machine learning models during post-processing are a promising baseline for more integrated developments, where the models will interact in a dynamic fashion with the flow solver to further improve coarse grid simulations.

  Abstract
  Computational fluid dynamics is a cornerstone for the modern aerospace industry, providing important insights on aerodynamic analysis while reducing the need of expensive [...]

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• SPDE-ConvNet: Predict stabilization parameter for Singularly Perturbed Partial Differential Equation

  S. Yadav, S. Ganesan

  eccomas2022.

  
  

  Abstract

  Singularly Perturbed Partial Differential Equations are challenging to solve with conventional numerical techniques such as Finite Element Methods due to the presence of boundary and interior layers. Often the standard numerical solution has spurious oscillations in the vicinity of these layers. Stabilization techniques are employed to eliminate these spurious oscillations in the numerical solution. The accuracy of the stabilization technique depends on a user-chosen stabilization parameter, where an optimal value is challenging to find. In this work, we focus on predicting an optimal value of the stabilization parameter for a stabilization technique called the Streamline Upwind Petrov Galerkin technique for solving singularly perturbed partial differential equations. This paper proposes SPDE-ConvNet, a convolutional neural network for predicting stabilization parameters by minimizing a loss based on the cross-wind derivative term. The proposed technique is compared with the state-of-the-art variational form-based neural network schemes.

  Abstract
  Singularly Perturbed Partial Differential Equations are challenging to solve with conventional numerical techniques such as Finite Element Methods due to the presence of boundary [...]

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• Simulation of massively separated flows and rotating machine flows using hybrid models

  F. Miralles, B. Sauvage, A. Duben, V. Bobkov, T. Kozubskaya, S. Wornom, B. Koobus, A. Dervieux

  eccomas2022.

  
  

  Abstract

  RANS, DES, hybrid RANS/DVMS and DDES/DVMS models are introduced in low dissipation schemes. They are compared for the simulation of vortex shedding flows around a NACA0021 at high angle of attack and a Caradonna-Tung helix.

  Abstract
  RANS, DES, hybrid RANS/DVMS and DDES/DVMS models are introduced in low dissipation schemes. They are compared for the simulation of vortex shedding flows around a NACA0021 [...]

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• Matrix properties associated with discrete conservation in flow simulations

  A. Veldman, G. Coppola

  eccomas2022.

  
  

  Abstract

  Supraconservative discretization methods are studied which conserve primary (mass, momentum and internal energy) as well as secondary (total energy) invariants. In particular, the coefficient matrices which are related to such conservation properties are analyzed. This analysis holds for any discretization method with a volume-consistent scaling.

  Abstract
  Supraconservative discretization methods are studied which conserve primary (mass, momentum and internal energy) as well as secondary (total energy) invariants. In particular, [...]

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