1,721,032 research outputs found
FULLY-DISCRETE ENTROPY CONSERVING/STABLE DISCONTINUOUS GALERKIN SOLVER FOR UNSTEADY COMPRESSIBLE VISCOUS FLOWS
No full textThe 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
On the kinematics and dynamics parameters governing the flow in oscillating foils
Full text linkBased on a high-order implicit discontinuous Galerkin method, numerical simulations of a two-dimensional oscillating foil are performed to explore the origin of basic aspects of the flow such as the generation of interesting flow structures in the wake and the associated aerodynamic forces. Dimensional arguments suggest that the flow is characterized by non dimensional aerodynamic coefficients depending on the kinematics of the oscillation, such its frequency and amplitude, and on the dynamics of the flow, such as the Reynolds number. Most of the studies have concentrated their attention on the role played by the kinematic of the oscillation with less or no attention to the effect of the Reynolds number. Here, we show that this effect cannot be neglected in the study of the phenomena at the basis of the generation of lift and thrust. We found that the Reynolds number plays a fundamental role for the development of thrust by defining critical values Rec for the switch from drag to thrust conditions. It is also shown that for Re>Rec, the Reynolds number defines additional subcritical values which are at the basis of flow instabilities leading to smooth and sharp transitions of the structure of the wake and of the related aerodynamic forces. For the analysis of the behaviour of the flow, the space of phases composed by the instantaneous lift and thrust (cL,cT) is introduced. It is shown how the orbits in the (cL,cT)-space allow us for a clear understanding of the physical evolution of the flow system and of the cyclical phenomena composing it
Visible Learning and synchronous online lesson in higher education: a study in engineering education
No full textThe Visible Learning (VL) approach to learning processes stems from Hattie's work based on synthesising meta-analyses regarding achievement in education. Although the model is used at many levels of instruction, its performance has been less studied in higher education, engineering education, and in the context of synchronous online learning in distance education. This study implements VL features and analyzes their ability to improve learning outcomes and teaching quality. To this end, a synchronous online lesson in a Fluid Dynamics course was implemented with 39 mechanical engineering students. The research method is a one-group pretest-posttest design and data were collected through a test and a 5-point Likert scale questionnaire. The learning achievement is measured using Cohen's d. The relevant effect size value obtained (d =2.32) stands out from those in the literature where meta-meta-analyses report an impact on learning close to that of a traditional lecture (d=0.08). Regarding the learning experience, students' ratings of both the lesson and the teacher's teaching quality are clearly positive. It can be concluded that the VL approach can produce significant learning gains and positive perceptions of instructional quality among students in the context of synchronous online instruction in engineering education
Entropy conserving implicit time integration in a Discontinuous Galerkin solver in entropy variables
No full textThis article presents a fully discrete entropy conserving/stable method based on a Discontinuous Galerkin (DG) discretization in entropy variables coupled with a modified Crank-Nicolson scheme. The entropy conserving time integration is inspired by the work of LeFloch [1], originally developed in the context of a Finite Volume method in conservative variables. This entropy conserving time integrator is here adapted to a DG discretization in entropy variables also demonstrating the fulfilment of entropy conservation regardless of the time step size and the type of elements used (quadrangular or triangular elements, possibly with curved edges). The performance of the implicit method will be demonstrated by computing several inviscid flow problems, i.e., the convection of an isentropic vortex, the double shear layer, the Kelvin-Helmholtz instability, the shedding flow past a triangular wedge, the Sod shock tube, the receding flow and the Taylor-Green vortex.(c) 2022 Elsevier Inc. All rights reserved
Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations
Full text linkThis work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner
P-multigrid preconditioners applied to high-order DG and HDG discretizations
No full textIn this work the use of a p-multigrid preconditioned flexible GMRES solver to deal with the solution of stiff linear systems arising from high order time discretization is explored in the context of two high-order spatial discretizations. The first one is a standard modal discontinuous Galerkin method, while the second one is an hybridizable discontinuous Galerkin method, which for high order has fewer globally-coupled degrees of freedom compared to DG. The efficiency of the proposed solution strategy is assessed on low-Mach, two-dimensional, compressible flow problems. The numerical results highlight that a considerable reduction in the number of GMRES iterations can be achieved for both space discretizations, but that only with DG is this gain reflected in the CPU time. Moreover, a comparison of the performance shed light on the convenience of using the former or the latter space discretization
Fully Discrete Entropy Conserving/Stable Discontinuous Galerkin Discretization of the Euler Equations in Entropy Variables
No full textAlgebraic modifications of the k-ω̃ and Spalart–Allmaras turbulence models to predict bypass and separation-induced transition
Full text linkMany reliable and robust turbulence models are nowadays available for the Reynolds-Averaged Navier-Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not suited to correctly described flows with low to moderate Reynolds numbers, which are characterized by strong transitional phenomena. Therefore, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models for the efficient design of many industrial applications. The only ways to describe transition are Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and transition models, where the computational cost of DNS and LES is still too high for their routine use in industry. A modified version of the k-(omega) over tilde and Spalart-Allmaras turbulence models is here proposed to predict transition due to the bypass and separation-induced modes. The modifications are based on the gamma k-(omega) over tilde and the SA-BCM models and avoid complex formulations of transport equations ad-hoc defined for transition. Both the transition models are correlation-based algebraic models that rely only on local flow information and an intermittency function, which damps the turbulent production according to some transition onset requirements. The proposed transition models are implemented in a high-order discontinuous Galerkin (dG) solver and validated on benchmark cases from the ERCOFTAC suite to the Eppler 387 airfoil, with different transition mode, freestream Reynolds number and turbulent intensity, and pressure gradient
High-order DG solutions of separating and reattaching flows
No full textWe report high-order implicit Large Eddy Simulations of flows around elongated bluff bodies with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leading-edge corners and the presence or not of a trailing-edge flow separation, on the behaviour of the initially laminar recirculating flow. Attention will be devoted also on the possible repercussions of such a results on the understanding of the nature of the main unsteadinesses of separating and reattaching flows. We finally prove the computational efficiency and the reliability of the proposed solution strategy for the time implicit high-order Discontinuous Galerkin (DG) discretization of the three-dimensional incompressible Navier-Stokes equations. The algorithm uses a linearly implicit Runge-Kutta scheme of the Rosenbrock type, and a p-multigrid preconditioned matrix-free linear solver
An implicit discontinuous galerkin method with reduced memory footprint for the simulation of turbulent flows
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