scholarly journals Assessment of a Discontinuous Galerkin Method for the Simulation of the Turbulent Flow around the DrivAer Car Model

2021 ◽  
Vol 11 (21) ◽  
pp. 10202
Author(s):  
Alessandro Colombo ◽  
Andrea Bortoli ◽  
Pierangelo Conti ◽  
Andrea Crivellini ◽  
Antonio Ghidoni ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Discontinuous Galerkin ◽  
Physical Phenomenon ◽  
Accurate Determination ◽  
Computational Cost ◽  
Scale Model ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
High Fidelity ◽  
Dg Method

The turbulent flow over the DrivAer fastback model is here investigated with an order-adaptive discontinuous Galerkin (DG) method. The growing need of high-fidelity flow simulations for the accurate determination of problems, e.g., vehicle aerodynamics, promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the large-eddy simulation (LES), to an industrial level. An appealing choice for SRS is the Implicit LES (ILES) via a high-order DG method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. Implicit time integration and the p-adaptive algorithm reduce the computational cost allowing a high-fidelity description of the physical phenomenon with very coarse mesh and moderate number of degrees of freedom. Two different models have been considered: (i) a simplified DrivAer fastback model, without the rear-view mirrors and the wheels, and a smooth underbody; (ii) the DrivAer fastback model, without rear-view mirrors and a smooth underbody. The predicted results have been compared with experimental data and CFD reference results, showing a good agreement.

scholarly journals A discontinuous Galerkin fast-sweeping eikonal solver for fast and accurate traveltime computation in 3D tilted anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C107-C118 ◽  
Author(s):  
Philippe Le Bouteiller ◽  
Mondher Benjemaa ◽  
Ludovic Métivier ◽  
Jean Virieux
Keyword(s):  
Discontinuous Galerkin ◽  
Seismic Anisotropy ◽  
Computational Cost ◽  
Anisotropic Media ◽  
Finite Difference Schemes ◽  
Seismic Amplitude ◽  
Fast Sweeping ◽  
Complex Models ◽  
Dg Method ◽  
Sweeping Method

We tackle the challenging problem of efficient and accurate seismic traveltime computation in 3D anisotropic media by applying the fast-sweeping method to a discontinuous Galerkin (DG)-based eikonal solver. Using this method leads to a stable and highly accurate scheme, which is faster than finite-difference schemes for a given precision, and with a low computational cost compared to the standard Runge-Kutta DG formulation. The integral formulation of the DG method also makes it easy to handle seismic anisotropy and complex topographies. Several numerical tests on complex models, such as the 3D SEG advanced modeling model, are given as illustration, highlighting the efficiency and the accuracy of this new approach. In the near future, these results will be used together with accurate solvers for seismic amplitude and take-off angle computation to revisit asymptotic inversion (traveltime/slope tomography) and imaging approaches (quantitative migration involving amplitudes and angles).

Basic Numerical Assessments to Perform a Quasi-Complete LES Toward IC-Engine Applications

2010 ◽  
Author(s):  
Federico Brusiani ◽  
Gian Marco Bianchi
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Computational Cost ◽  
Step Test ◽  
Scale Model ◽  
Numerical Representation ◽  
Mean Flow ◽  
Ic Engine ◽  
Simulation Methodology ◽  
Turbulent Scales

Still today, the numerical representation of a fully 3D turbulent flow remains one of the most challenging task. In Computational Fluid Dynamics (CFD), turbulent flows can be numerically solved with different levels of accuracy bounded between Reynolds Averaged Navier Stokes (RANS) and Direct Numerical Simulation (DNS) methods. Today, the RANS is the standard approach to perform turbulent flow simulations. It allows a good reproduction of the mean flow conditions guaranteeing, at the same time, an acceptable computational cost for practical engineering applications. Unlike the RANS, DNS is the most complete approach that can be used to numerically solve a turbulent flow because, in this case, all the turbulent scales are directly solved. However, today the DNS approach remains inapplicable in industrial field because of the prohibitive computational power required. Between RANS and DNS, a third method can be considered for the solution of high Reynolds turbulent flows: Large Eddy Simulation (LES). LES approach allows the direct solution of the largest turbulent scales (anisotropy turbulence) while the smallest scales (isotropy turbulence) are numerically modelled by a sub-grid scale model. For this reason, with respect to RANS, LES is expected to give an improvement about turbulent flow numerical solution when the physical behaviour of the considered fluid domain is dominated by the large scales of motion. At the same time, the computational cost of a LES simulation is quite lower than for DNS simulation. Even if during the last years LES has helped to improve the comprehension of complex turbulent fluid dynamic systems, for its applications in industrial fields further insights are needed. In particular, one of the main problem linked to the LES method regards the definition of a simulation methodology by which to obtain an high solution level (i.e. high level of energy directly solved) at the lowest computational cost. To fulfill this requirement, the authors defined a new LES simulation methodology based on Adaptive Mesh Refinement (AMR). The first results obtained by its application on a backward facing step test case are here presented and discussed in detail.

Runge-Kutta Central Discontinuous Galerkin Methods for the Special Relativistic Hydrodynamics

2017 ◽  
Vol 22 (3) ◽  
pp. 643-682 ◽  
Author(s):  
Jian Zhao ◽  
Huazhong Tang
Keyword(s):  
Discontinuous Galerkin ◽  
Computational Cost ◽  
Approximate Solutions ◽  
Two Dimensions ◽  
Numerical Dissipation ◽  
Test Problems ◽  
Runge Kutta ◽  
The One ◽  
Original Cell ◽  
Central Discontinuous Galerkin

AbstractThis paper develops Runge-Kutta PK-based central discontinuous Galerkin (CDG) methods with WENO limiter for the one- and two-dimensional special relativistic hydrodynamical (RHD) equations, K = 1,2,3. Different from the non-central DG methods, the Runge-Kutta CDG methods have to find two approximate solutions defined on mutually dual meshes. For each mesh, the CDG approximate solutions on its dual mesh are used to calculate the flux values in the cell and on the cell boundary so that the approximate solutions on mutually dual meshes are coupled with each other, and the use of numerical flux will be avoided. The WENO limiter is adaptively implemented via two steps: the “troubled” cells are first identified by using a modified TVB minmod function, and then the WENO technique is used to locally reconstruct new polynomials of degree (2K+1) replacing the CDG solutions inside the “troubled” cells by the cell average values of the CDG solutions in the neighboring cells as well as the original cell averages of the “troubled” cells. Because the WENO limiter is only employed for finite “troubled” cells, the computational cost can be as little as possible. The accuracy of the CDG without the numerical dissipation is analyzed and calculation of the flux integrals over the cells is also addressed. Several test problems in one and two dimensions are solved by using our Runge-Kutta CDG methods with WENO limiter. The computations demonstrate that our methods are stable, accurate, and robust in solving complex RHD problems.

Message Passing Neural Networks for Partial Charge Assignment to Metal-Organic Frameworks

2020 ◽  
Author(s):  
Ali Raza ◽  
Arni Sturluson ◽  
Cory Simon ◽  
Xiaoli Fern
Keyword(s):  
Electronic Structure ◽  
Message Passing ◽  
Gas Adsorption ◽  
Metal Organic Frameworks ◽  
Computational Cost ◽  
Electronic Structure Calculations ◽  
High Fidelity ◽  
Partial Charges ◽  
Metal Organic ◽  
Structure Calculations

Virtual screenings can accelerate and reduce the cost of discovering metal-organic frameworks (MOFs) for their applications in gas storage, separation, and sensing. In molecular simulations of gas adsorption/diffusion in MOFs, the adsorbate-MOF electrostatic interaction is typically modeled by placing partial point charges on the atoms of the MOF. For the virtual screening of large libraries of MOFs, it is critical to develop computationally inexpensive methods to assign atomic partial charges to MOFs that accurately reproduce the electrostatic potential in their pores. Herein, we design and train a message passing neural network (MPNN) to predict the atomic partial charges on MOFs under a charge neutral constraint. A set of ca. 2,250 MOFs labeled with high-fidelity partial charges, derived from periodic electronic structure calculations, serves as training examples. In an end-to-end manner, from charge-labeled crystal graphs representing MOFs, our MPNN machine-learns features of the local bonding environments of the atoms and learns to predict partial atomic charges from these features. Our trained MPNN assigns high-fidelity partial point charges to MOFs with orders of magnitude lower computational cost than electronic structure calculations. To enhance the accuracy of virtual screenings of large libraries of MOFs for their adsorption-based applications, we make our trained MPNN model and MPNN-charge-assigned computation-ready, experimental MOF structures publicly available.<br>

A two-stage design optimization framework for multifield origami-inspired structures

2021 ◽  
pp. 1045389X2110116
Author(s):  
Wei Zhang ◽  
Saad Ahmed ◽  
Jonathan Hong ◽  
Zoubeida Ounaies ◽  
Mary Frecker
Keyword(s):  
Case Studies ◽  
Computing Time ◽  
Computational Cost ◽  
High Fidelity ◽  
Fe Model ◽  
Two Stage ◽  
Baseline Design ◽  
Optimization Framework ◽  
Highly Nonlinear ◽  
Stage 1

Different types of active materials have been used to actuate origami-inspired self-folding structures. To model the highly nonlinear deformation and material responses, as well as the coupled field equations and boundary conditions of such structures, high-fidelity models such as finite element (FE) models are needed but usually computationally expensive, which makes optimization intractable. In this paper, a computationally efficient two-stage optimization framework is developed as a systematic method for the multi-objective designs of such multifield self-folding structures where the deformations are concentrated in crease-like areas, active and passive materials are assumed to behave linearly, and low- and high-fidelity models of the structures can be developed. In Stage 1, low-fidelity models are used to determine the topology of the structure. At the end of Stage 1, a distance measure [Formula: see text] is applied as the metric to determine the best design, which then serves as the baseline design in Stage 2. In Stage 2, designs are further optimized from the baseline design with greatly reduced computing time compared to a full FEA-based topology optimization. The design framework is first described in a general formulation. To demonstrate its efficacy, this framework is implemented in two case studies, namely, a three-finger soft gripper actuated using a PVDF-based terpolymer, and a 3D multifield example actuated using both the terpolymer and a magneto-active elastomer, where the key steps are elaborated in detail, including the variable filter, metrics to select the best design, determination of design domains, and material conversion methods from low- to high-fidelity models. In this paper, analytical models and rigid body dynamic models are developed as the low-fidelity models for the terpolymer- and MAE-based actuations, respectively, and the FE model of the MAE-based actuation is generalized from previous work. Additional generalizable techniques to further reduce the computational cost are elaborated. As a result, designs with better overall performance than the baseline design were achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the multifield example, which would rather be over 3 and 2 months for full FEA-based optimizations, respectively. Tradeoffs between the competing design objectives were achieved. In both case studies, the efficacy and computational efficiency of the two-stage optimization framework are successfully demonstrated.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

Large eddy simulation study of turbulent flow around smooth and rough domes

2013 ◽  
Vol 227 (12) ◽  
pp. 2686-2700 ◽  
Author(s):  
N Kharoua ◽  
L Khezzar
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flow ◽  
Flow Behavior ◽  
Pressure Coefficient ◽  
Horseshoe Vortex ◽  
Scale Model ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Large Eddy

Large eddy simulation of turbulent flow around smooth and rough hemispherical domes was conducted. The roughness of the rough dome was generated by a special approach using quadrilateral solid blocks placed alternately on the dome surface. It was shown that this approach is capable of generating the roughness effect with a relative success. The subgrid-scale model based on the transport of the subgrid turbulent kinetic energy was used to account for the small scales effect not resolved by large eddy simulation. The turbulent flow was simulated at a subcritical Reynolds number based on the approach free stream velocity, air properties, and dome diameter of 1.4 × 105. Profiles of mean pressure coefficient, mean velocity, and its root mean square were predicted with good accuracy. The comparison between the two domes showed different flow behavior around them. A flattened horseshoe vortex was observed to develop around the rough dome at larger distance compared with the smooth dome. The separation phenomenon occurs before the apex of the rough dome while for the smooth dome it is shifted forward. The turbulence-affected region in the wake was larger for the rough dome.

Differences in the Upscaling Procedure for Compositional Reservoir Simulations of Immiscible and Miscible Gas Flooding

2021 ◽  
Author(s):  
Victor de Souza Rios ◽  
Arne Skauge ◽  
Ken Sorbie ◽  
Gang Wang ◽  
Denis José Schiozer ◽  
...  
Keyword(s):  
Computational Cost ◽  
Specific Treatment ◽  
Dynamic Responses ◽  
Scale Model ◽  
Small Scale ◽  
Coarse Scale ◽  
Reservoir Models ◽  
Permeability Upscaling ◽  
Gas Flooding ◽  
Grid Block

Abstract Compositional reservoir simulation is essential to represent the complex interactions associated with gas flooding processes. Generally, an improved description of such small-scale phenomena requires the use of very detailed reservoir models, which impact the computational cost. We provide a practical and general upscaling procedure to guide a robust selection of the upscaling approaches considering the nature and limitations of each reservoir model, exploring the differences between the upscaling of immiscible and miscible gas injection problems. We highlight the different challenges to achieve improved upscaled models for immiscible and miscible gas displacement conditions with a stepwise workflow. We first identify the need for a special permeability upscaling technique to improve the representation of the main reservoir heterogeneities and sub-grid features, smoothed during the upscaling process. Then, we verify if the use of pseudo-functions is necessary to correct the multiphase flow dynamic behavior. At this stage, different pseudoization approaches are recommended according to the miscibility conditions of the problem. This study evaluates highly heterogeneous reservoir models submitted to immiscible and miscible gas flooding. The fine models represent a small part of a reservoir with a highly refined set of grid-block cells, with 5 × 5 cm2 area. The upscaled coarse models present grid-block cells of 8 × 10 m2 area, which is compatible with a refined geological model in reservoir engineering studies. This process results in a challenging upscaling ratio of 32 000. We show a consistent procedure to achieve reliable results with the coarse-scale model under the different miscibility conditions. For immiscible displacement situations, accurate results can be obtained with the coarse models after a proper permeability upscaling procedure and the use of pseudo-relative permeability curves to improve the dynamic responses. Miscible displacements, however, requires a specific treatment of the fluid modeling process to overcome the limitations arising from the thermodynamic equilibrium assumption. For all the situations, the workflow can lead to a robust choice of techniques to satisfactorily improve the coarse-scale simulation results. Our approach works on two fronts. (1) We apply a dual-porosity/dual-permeability upscaling process, developed by Rios et al. (2020a), to enable the representation of sub-grid heterogeneities in the coarse-scale model, providing consistent improvements on the upscaling results. (2) We generate specific pseudo-functions according to the miscibility conditions of the gas flooding process. We developed a stepwise procedure to deal with the upscaling problems consistently and to enable a better understanding of the coarsening process.

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