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Register a new userOn the ability of discontinuous Galerkin methods to simulate under-resolved turbulent flows
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We investigate the ability of discontinuous Galerkin (DG) methods to simulate under-resolved turbulent flows in large-eddy simulation. The role of the Riemann solver and the subgrid-scale model in the prediction of a variety of flow regimes, including transition to turbulence, wall-free turbulence and wall-bounded turbulence, are examined. Numerical and theoretical results show the Riemann solver in the DG scheme plays the role of an implicit subgrid-scale model and introduces numerical dissipation in under-resolved turbulent regions of the flow. This implicit model behaves like a dynamic model and vanishes for flows that do not contain subgrid scales, such as laminar flows, which is a critical feature to accurately predict transition to turbulence. In addition, for the moderate-Reynolds-number turbulence problems considered, the implicit model provides a more accurate representation of the actual subgrid scales in the flow than state-of-the-art explicit eddy viscosity models, including dynamic Smagorinsky, WALE and Vreman. The results in this paper indicate new best practices for subgrid-scale modeling are needed with high-order DG methods.
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We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method inherits the advantages of both the EDG method and the HDG method to make itself well-suited for turbulence simulations. We propose a minimal residual Newton algorithm for solving the nonlinear system arising from the IEDG discretization of the Navier-Stokes equations. The preconditioned GMRES algorithm is based on a restricted additive Schwarz (RAS) preconditioner in conjunction with a block incomplete LU factorization at the subdomain level. The proposed approach is applied to the ILES of transitional turbulent flows over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both design and off-design conditions. The high-order ILES results show good agreement with a subgrid-scale LES model discretized with a second-order finite volume code while using significantly less degrees of freedom. This work shows that high-order accuracy is key for predicting transitional turbulent flows without a SGS model.
The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the Navier-Stokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines Newtons method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that Stream Upwind Petrov-Galerkin regularization approach is required to solve properly the ill-posed Buongiorno transport model being tackled as a variational problem under mean value constraint. Non-trivial numerical computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature. The numerical experiments demonstrate that by accounting for only the thermophoresis and Brownian motion forces in the concentration transport equation, the model is not able to reproduce the heat transfer impairment due to the presence of suspended nanoparticles in the base fluid. It reveals, however, the significant role that these two terms play in the vicinity of the hot and cold walls.
On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for the spatiotemporal dynamics in the plane of the flow. Truncating this set beyond lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at cruder effective wall-normal resolution. Perspectives opened by the approach are discussed.
The physical processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. Here, we use an approach based on instanton theory for the velocity increment dynamics through scales. Cascade trajectories with negative stochastic thermodynamics entropy exchange values lead to anomalous increments at small-scales. These trajectories concentrate around an instanton, which is the minimum of an effective action produced by turbulent fluctuations. The connection between entropy from stochastic thermodynamics and the related instanton provides a new perspective on the cascade process and the intermittency phenomenon.
It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability) and barriers (low permeability) for flows in heterogeneous porous media. We propose here new interface spaces, which are based on physics, to deal with permeability fields in the simultaneous presence of fractures and barriers, accommodated respectively, by the pressure and flux spaces. Existing multiscale methods based on mixed formulations can take advantage of the proposed interface spaces, however, in order to present and test our results, we use the newly developed Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], which generalizes most well-known multiscale mixed methods, and allows for the independent choice of the pressure and flux interface spaces. An adaptive version of the MRCM [Rocha, et al., J. Comput. Phys., 409 (2020), 109316] is considered that automatically selects the physics-based pressure space for fractured structures and the physics-based flux space for regions with barriers, resulting in a procedure with unprecedented accuracy. The features of the proposed approach are investigated through several numerical simulations of single-phase and two-phase flows, in different heterogeneous porous media. The adaptive MRCM combined with the interface spaces based on physics provides promising results for challenging problems with the simultaneous presence of fractures and barriers.
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