Theory and Applications of High-Order Methods in Computational Fluid Dynamics

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (15 April 2022) | Viewed by 13786

Special Issue Editor


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Guest Editor
Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Armii Krajowej 21, 42-201 Czestochowa, Poland
Interests: numerical methods; high-order schemes; turbulence modelling; high-performance computing; two-phase flows; combustion modelling; flow control; LES/DNS

Special Issue Information

Dear Colleagues,

Over the few last decades, CFD (computational fluid dynamics) has become a powerful tool in fluid dynamics research in all possible branches (turbulence, two-phase and reactive flows, flow control, etc.), not only in academia but also in scientific centers and industry. The rapid development of high-performance computers and high-order discretization methods (HOMs) opens new horizons for better understanding phenomena that were previously hidden by limited modeling capabilities. Although the classical finite volume/finite element type methods are irreplaceable in practical applications, they cannot compete with the HOMs in advanced CFD investigations, including DNS (direct numerical simulation) and LES (large eddy simulation). In terms of their solution accuracy, the spectral and pseudo-spectral methods are regarded as the most accurate, yet, they can only be applied in rather simple computational domains and with boundary conditions enforced by the method applied. For instance, the spectral method based on the Fourier series is suited for periodic problems. In these respects, HOMs based on compact stencils, such as discontinuous Galerkin, spectral difference/volume, residual distribution, flux reconstruction, and compact difference schemes provide more freedom. The forthcoming Special Issue focuses on the theory and applications of HOMs in complex geometries and/or for a deep understanding of fundamental flow phenomena. The main attention is put on the use and development of HOMs for turbulent reactive flows (combustion), laminar–turbulent transition, and passive/active flow control strategies, yet it is not limited to these problems. A common feature of modeling turbulent flames, transitional flows, and multi-scale flow control is a wide range of strongly unsteady turbulent scales, in which accurate representation on a numerical mesh is crucial for the solution accuracy. It is believed that the present Special Issue will prove that HOMs ensure this in the most efficient way.

Prof. Dr. Artur Tyliszczak
Guest Editor

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Keywords

  • high-order discretization methods
  • reactive flows
  • near-wall flows
  • flow control
  • numerical/modeling error interactions

Published Papers (6 papers)

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Research

18 pages, 5309 KiB  
Article
Influence of the Mesh Topology on the Accuracy of Modelling Turbulent Natural and Excited Round Jets at Different Initial Turbulence Intensities
by Karol Wawrzak and Artur Tyliszczak
Appl. Sci. 2022, 12(21), 11244; https://doi.org/10.3390/app122111244 - 06 Nov 2022
Cited by 3 | Viewed by 961
Abstract
The paper is aimed at an assessment of the importance of the coordinate system (Cartesian vs. cylindrical) assumed for simulations of free-round jets. The research is performed by applying the large eddy simulation method with spatial discretisation based on high-order compact difference schemes. [...] Read more.
The paper is aimed at an assessment of the importance of the coordinate system (Cartesian vs. cylindrical) assumed for simulations of free-round jets. The research is performed by applying the large eddy simulation method with spatial discretisation based on high-order compact difference schemes. The results obtained for natural and excited jets at three different turbulence intensity levels, Ti=0.01%,0.1% and 1.0%, are compared. In the case of the natural jet, it is found that both instantaneous and time-averaged results are significantly dependent on the coordinate system only for the lowest Ti. In this case, in the Cartesian coordinate system, the errors introduced by an azimuthal non-uniformity of the mesh seem to have a larger impact on the solutions than the disturbances generated at the nozzle exit. The azimuthal non-uniformity of the mesh also has a substantial influence on the results of the modelling of the excited jets. In this case, the excitation is introduced as time-varying forcing, with the frequency corresponding to half of the preferred mode frequency and the amplitude equal to 5% of the jet velocity. Such an excitation leads to the formation of the so-called side-jets being revealed as inclined streams of fluid ejected outside the main jet stream. Primary attention is paid to the mechanism of the formation of the side-jets, their number and location. The results obtained on Cartesian meshes show that for very low turbulence intensity levels (Ti=0.01%), the number and direction of the side-jets are dependent on the non-uniform distribution of the mesh nodes along the azimuthal direction of the jet. On the other hand, when the cylindrical coordinate system is used, the number of the side-jets and their locations are random and dependent only on inlet parameters. It has been demonstrated that the mechanism of side-jet formation is the same in both coordinate systems; however, its random nature can only be predicted when the cylindrical coordinate system is used. Full article
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24 pages, 990 KiB  
Article
Assessment of an Implicit Discontinuous Galerkin Solver for Incompressible Flow Problems with Variable Density
by Francesco Bassi, Lorenzo Alessio Botti, Alessandro Colombo and Francesco Carlo Massa
Appl. Sci. 2022, 12(21), 11229; https://doi.org/10.3390/app122111229 - 05 Nov 2022
Viewed by 1175
Abstract
Multi-component flow problems are typical of many technological and engineering applications. In this work, we propose an implicit high-order discontinuous Galerkin discretization of the variable density incompressible (VDI) flow model for the simulation of multi-component problems. Indeed, the peculiarity of the VDI model [...] Read more.
Multi-component flow problems are typical of many technological and engineering applications. In this work, we propose an implicit high-order discontinuous Galerkin discretization of the variable density incompressible (VDI) flow model for the simulation of multi-component problems. Indeed, the peculiarity of the VDI model is that the density is treated as an advected property, which can be used to possibly track multiple (more than two) components. The interface between fluids is described by a smooth, but sharp, variation in the density field, thus not requiring any geometrical reconstruction. Godunov numerical fluxes, density positivity, mass conservation, and Gibbs-type phenomena at material interfaces are challenges that are considered during the numerical approach development. To avoid Courant-related time step restrictions, high-order single-step multi-stage implicit schemes are applied for the temporal integration. Several test cases with known analytical solutions are used to assess the current approach in terms of space, time, and mass conservation accuracy. As a challenging application, the simulation of a 2D droplet impinging on a thin liquid film is performed and shows the capabilities of the proposed DG approach when dealing with high-density (water–air) multi-component problems. Full article
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15 pages, 6186 KiB  
Article
Numerical and Experimental Validation of a Supersonic Mixing Layer Facility
by Yudong Li, Li Chen, Hongxun Li, Yungang Wu and Shuang Chen
Appl. Sci. 2022, 12(11), 5489; https://doi.org/10.3390/app12115489 - 28 May 2022
Cited by 2 | Viewed by 1302
Abstract
The design of a supersonic-supersonic mixing layer facility was motivated by the need for a benchmark experimental platform to study the physical phenomena underlying supersonic mixing layers. The facility is an intermittent blowdown wind tunnel characterized by a two-stream design separated by a [...] Read more.
The design of a supersonic-supersonic mixing layer facility was motivated by the need for a benchmark experimental platform to study the physical phenomena underlying supersonic mixing layers. The facility is an intermittent blowdown wind tunnel characterized by a two-stream design separated by a splitter plate in the middle of the nozzle. The splitter plate ends exactly at the start of the mixing layer test section. The Mach number of the primary stream is M1 = 3 for all nozzles and the secondary streams are M2 = 2, 2.5, and 2.9 to generate different convective Mach numbers of Mc = 0.25, 0.10, and 0.01, respectively. The facility was calibrated by pressure measurements to verify the Mach number and the pressure distribution in the streamwise direction. Large-eddy simulation (LES) was performed to illustrate a full view of the turbulent compressible mixing layer flow field and to compare this against the experimental data. Optical diagnosis measurements, i.e., femtosecond laser-induced electronic excitation tagging velocimetry (FLEET) for velocity measurement and focused laser differential interferometer (FLDI) for the density fluctuation, were also performed on the facility. Full article
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21 pages, 16779 KiB  
Article
A Numerical Aerodynamic Analysis on the Effect of Rear Underbody Diffusers on Road Cars
by Alex Guerrero, Robert Castilla and Giorgio Eid
Appl. Sci. 2022, 12(8), 3763; https://doi.org/10.3390/app12083763 - 08 Apr 2022
Cited by 10 | Viewed by 6312
Abstract
The aerodynamic complexity of the underbody surfaces of conventional road vehicles is a matter of fact. Currently available literature is focused mainly on very simple Ahmed-body geometries as opposed to realistic car shapes, due to their complexity and computational cost. We attempted to [...] Read more.
The aerodynamic complexity of the underbody surfaces of conventional road vehicles is a matter of fact. Currently available literature is focused mainly on very simple Ahmed-body geometries as opposed to realistic car shapes, due to their complexity and computational cost. We attempted to understand the flow behaviour around different realistic conventional road car geometries, and we provide an extensive evaluation of the aerodynamic loads generated. The key findings of this article could potentially set a precedent and be useful within the automotive industry’s investigations on drag-reduction mechanisms or sources of downforce generation. The novelty of the work resides in the realistic approach employed for the geometries and in the investigation of barely researched aerodynamic elements, such as front diffusers, which might pave the way for further research studies. A baseline flat-underfloor design, a 7 venturi diffuser-equipped setup, a venturi diffuser with diagonal skirts, and the same venturi diffuser with frontal slot-diffusers are the main configurations we studied. The numerical predictions evaluated using RANS computational fluid dynamics (CFD) simulations deal with the aerodynamic coefficients. The configuration that produced the highest downforce coefficient was the one composed of the 7 venturi diffuser equipped with diagonal sealing skirts, achieving a CL value of −0.887, which represents an increase of around 1780% with regard to the baseline model. That achievement and the gains in higher vertical loads also entail a compromise with an increase in the overall air resistance. The performance achieved with diffusers in the generation of downforce is, as opposed to the one obtained with conventional wings, a cleaner alternative, by avoiding wake disturbances and downwash phenomena. Full article
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18 pages, 1654 KiB  
Article
Application of High-Order Compact Difference Schemes for Solving Partial Differential Equations with High-Order Derivatives
by Lena Caban and Artur Tyliszczak
Appl. Sci. 2022, 12(4), 2203; https://doi.org/10.3390/app12042203 - 20 Feb 2022
Cited by 1 | Viewed by 1655
Abstract
In this paper, high-order compact-difference schemes involving a large number of mesh points in the computational stencils are used to numerically solve partial differential equations containing high-order derivatives. The test cases include a linear dispersive wave equation, the non-linear Korteweg–de Vries (KdV)-like equations, [...] Read more.
In this paper, high-order compact-difference schemes involving a large number of mesh points in the computational stencils are used to numerically solve partial differential equations containing high-order derivatives. The test cases include a linear dispersive wave equation, the non-linear Korteweg–de Vries (KdV)-like equations, and the non-linear Kuramoto–Sivashinsky equation with known analytical solutions. It is shown that very high-order compact schemes, e.g., of 20th or 24th orders, cause a very fast drop in the L2 norm error, which in some cases reaches a machine precision already on relatively coarse computational meshes. Full article
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19 pages, 24833 KiB  
Article
Assessment of a Discontinuous Galerkin Method for the Simulation of the Turbulent Flow around the DrivAer Car Model
by Alessandro Colombo, Andrea Bortoli, Pierangelo Conti, Andrea Crivellini, Antonio Ghidoni, Alessandra Nigro and Gianmaria Noventa
Appl. Sci. 2021, 11(21), 10202; https://doi.org/10.3390/app112110202 - 31 Oct 2021
Cited by 1 | Viewed by 1603
Abstract
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 [...] Read more.
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. Full article
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