A Symmetry-Preserving Discretization and Regularization Subgrid Model for Compressible Turbulent Flow

Volume 1A, Symposia: Advances in Fluids Engineering Education; Turbomachinery Flow Predictions and Optimization; Applications I

Kok

Verstappen

et al. 2014

A fourth-order accurate symmetry-preserving discretization for compressible flow is used to perform simulations of the turbulent flow over a delta wing. A symmetry-preserving discretization eliminates the non-linear convective instability by preserving conservation of kinetic energy at the discrete level. This enhances the stability of a simulation method, so that little artificial dissipation is needed for numerical stability. It is shown that simulations of the flow over a sharp-edge delta wing at Re = 50,000 with the symmetry-preserving discretization are stable without artificial dissipation in a region of interest around the delta wing. To assess the accuracy of the simulation method, results obtained on a fine computational grid are compared with results obtained on a coarser grid. Also results obtained with large-eddy simulation models and with sixth-order artificial dissipation are presented. * Corresponding author; w.rozema@rug.nl INTRODUCTIONPreserving conservation laws in a numerical method can be advantageous for solving differential equations from fluid dynamics. The Lax-Wendroff theorem, for example, states that preserving conservation at the discrete level together with convergence implies convergence to an actual weak solution [1]. From a practical point of view, preserving mass conservation in a discretization prevents numerical leakage of a fluid, and preserving conservation laws at the discrete level is important for computing shock waves with an appropriate propagation speed. Naturally finite-volume methods, which are derived from the integral form of the governing equations and preserve conservation laws by construction, are very popular in computational fluid dynamics.Preserving conservation properties in a simulation method is also advantageous for simulations of incompressible turbulence. Turbulence forms a cascade of progressively smaller flow structures. In practice it is often not possible to capture the full range of turbulent flow structures on the computational grid. Once the size of the smallest flow structures in the solution approaches the mesh spacing, the dynamics of these flow structures can no longer be accurately predicted. General finite-volume methods

Section: Methodsmentioning

confidence: 99%

Section: Time Integrationmentioning

confidence: 99%

Section: Symmetry-preserving Spatial Discretizationmentioning

confidence: 99%

Section: Symmetry-preserving Spatial Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

DNS and LES of the Compressible Flow Over a Delta Wing With the Symmetry-Preserving Discretization

Volume 1A, Symposia: Advances in Fluids Engineering Education; Turbomachinery Flow Predictions and Optimization; Applications I

Kok

Verstappen

et al. 2014

Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

Arch Computat Methods Eng

Verstappen

Veldman

et al. 2018

The simulation of turbulent flows by means of computational fluid dynamics is highly challenging. The costs of an accurate direct numerical simulation (DNS) are usually too high, and engineers typically resort to cheaper coarse-grained models of the flow, such as large-eddy simulation (LES). To be suitable for the computation of turbulence, methods should not numerically dissipate the turbulent flow structures. Therefore, energy-conserving discretizations are investigated, which do not dissipate energy and are inherently stable because the discrete convective terms cannot spuriously generate kinetic energy. They have been known for incompressible flow, but the development of such methods for compressible flow is more recent. This paper will focus on the latter: LES and DNS for turbulent subsonic flow. A new theoretical framework for the analysis of energy conservation in compressible flow is proposed, in a mathematical notation of square-root variables, inner products, and differential operator symmetries. As a result, the discrete equations exactly conserve not only the primary variables (mass, momentum and energy), but also the convective terms preserve (secondary) discrete kinetic and internal energy. Numerical experiments confirm that simulations are stable without the addition of artificial dissipation. Next, minimum-dissipation eddyviscosity models are reviewed, which try to minimize the dissipation needed for preventing sub-grid scales from polluting the numerical solution. A new model suitable for anisotropic grids is proposed: the anisotropic minimum-dissipation model. This model appropriately switches off for laminar and transitional flow, and is consistent with the exact sub-filter tensor on anisotropic grids. The methods and models are first assessed on several academic test cases: channel flow, homogeneous decaying turbulence and the temporal mixing layer. As a practical application, accurate simulations of the transitional flow over a delta wing have been performed. The Compressible Navier-Stokes Equations Primary ConservationOur objective is the development of simulation methods for aerodynamic flow, governed by the Navier-Stokes equations for compressible flow [21]:

Numerical simulation with low artificial dissipation of transitional flow over a delta wing

Journal of Computational Physics

Kok

Veldman

et al. 2020