Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImplicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method
116
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular meshes. The velocity distribution function and its trace are approximated in the piecewise polynomial space of degree up to 4. The fast spectral method (FSM) is incorporated into the DG discretization to evaluate the collision operator. Specific polynomial approximation is proposed for the collision term to reduce the computational cost. The proposed scheme is proved to be accurate and efficient.
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous generation of high wavenumber modes, which we term the $k_infty$ irregularity. In this work, an inviscid regularization technique called observable regularization is proposed for the simulation of two-phase compressible flows. The proposed approach regularizes the equations at the level of the partial differential equation and as a result, any numerical method can be used to solve the system of equations. The regularization is accomplished by introducing an observability limit that represents the length scale below which one cannot properly model or continue to resolve flow structures. An observable volume fraction equation is derived for capturing the material interface, which satisfies the pressure equilibrium at the interface. The efficacy of the observable regularization method is demonstrated using several test cases, including a one-dimensional material interface tracking, one-dimensional shock-tube and shock-bubble problems, and two-dimensional simulations of a shock interacting with a cylindrical bubble. The results show favorable agreement, both qualitatively and quantitatively, with available exact solutions or numerical and experimental data from the literature. The computational saving by using the current method is estimated to be about one order of magnitude in two-dimensional computations and significantly higher in three-dimensional computations. Lastly, the effect of the observability limit and best practices to choose its value are discussed.
In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for the 5-equation model of compressible multi-component flows with Mie-Gruneisen equation of state. The method mainly consists of three steps: firstly, the DG method with the non-oscillatory kinetic flux is used to solve the conservative equations of the model; secondly, inspired by Abgralls idea, we derive a DG scheme for the volume fraction equation which can avoid the unphysical oscillations near the material interfaces; finally, a multi-resolution WENO limiter and a maximum-principle-satisfying limiter are employed to ensure oscillation-free near the discontinuities, and preserve the physical bounds for the volume fraction, respectively. Numerical tests show that the method can achieve high order for smooth solutions and keep non-oscillatory at discontinuities. Moreover, the velocity and pressure are oscillation-free at the interface and the volume fraction can stay in the interval [0,1].
A new methodology based on energy flux similarity is suggested in this paper for large eddy simulation (LES) of transitional and turbulent flows. Existing knowledge reveals that the energy cascade generally exists in transitional and turbulent flows with different distributions, and the characteristic quantity of scale interaction in energy cascade processes is energy flux. Therefore, energy flux similarity is selected as the basic criterion to secure the flow field getting from LES highly similar to the real flow field. Through a priori tests, we find that the energy flux from the tensor-diffusivity (TD) model has high similarity with the real energy flux. Then, we modify the modelled energy flux from the TD model and obtain uniform formulas of energy flux similarity corresponding to different filter widths and locations in the wall-bounded turbulence. To secure the robustness of simulation and the LES results similar to the real flow, we apply the energy flux similarity method (EFSM) to the Smagorinsky model in the LES of compressible turbulent channel flow, compressible flat-plate flow, and flow over a compressible ramp. The a posteriori tests show that, overall, EFSM can better predict these flows than other subgrid-scale models. In the simulation of turbulent channel flow, EFSM can accurately predict the mean stream-wise velocity, Reynolds stress, and affluent coherent structures. In LES of compressible flat-plate flow, EFSM could provide accurate simulation results of the onset of transition and transition peak, skin friction, and mean stream-wise velocity in cases with three different grid scales. Meanwhile, for flow over a compressible ramp, EFSM could correctly describe the process of bypass transition, locations of separation and reattachment in the corner region, and abundant coherent vortex structures, etc.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
