Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

Abstract

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]:

Supra-Conservative Finite-Volume Methods for the Simulation of Subsonic Flow

“…No rigorous proof has been found yet for the general compressible case, but in practice this appears to be mainly a theoretical issue. Another 'reward' is that subtleties in (eddy-viscosity) turbulence models are not masked by excessive numerical dissipation [31,38]. To demonstrate the performance of the above methods, we point the reader to a number of papers that are successfully using them.…”

“…In fact, the latter requirement determines the choice of D mass ! The above discretization, (14) + (15) with interpolation (16), satisfies the main Requirement 1: C m mom − 1 2 diag(D mass m) is skew symmetric, for all choices of the mass fluxes m. There is some freedom left to use geometry information to interpolate from the values of m in the cell centers to the values of m at the faces [38].…”

Computational Methods for Moving and Deforming Objects in Extreme Waves

“…Here M is the divergence operator, which describes conservation of mass. Conservation of momentum is based on the convection operator C(u)v ≡ ∇(u ⊗ v), the pressure gradient operator G = ∇, the viscous diffusion operator V (u) ≡ ∇ • ν∇u and a forcing term f. The kinematic viscosity is denoted by ν. Turbulence is modelled by means of large-eddy simulation (LES) using a low-dissipation QR-model as formulated by Verstappen [20] and refined by Rozema [21][22][23]. For its use in maritime applications, see [24,25].…”

Preventing the Added-Mass Instability in Fluid-Solid Interaction for Offshore Applications

“…Here M is the divergence operator, which describes conservation of mass. Conservation of momentum is based on the convection operator C(u)v ≡ ∇(u ⊗ v), the pressure gradient operator G = ∇, the viscous diffusion operator V (u) ≡ ∇ • ν∇u and a forcing term f. The kinematic viscosity is denoted by ν. Turbulence is modelled by means of large-eddy simulation (LES) using a low-dissipation QR-model as formulated by Verstappen [13] and refined by Rozema [14][15][16]. For its use in maritime applications, see [17,18].…”

“…To understand the coupling problems, the stability of the two-way coupled system is investigated in an abstract setting. On both sides of the fluid-body interface Γ FS physical properties need to be continuous, as expressed in the kinematic and dynamic conditions (13) and (14). This makes it possible to formulate the coupling problem in terms of interface variables only: the velocity along the interface u Γ and the local or total load exerted by the fluid to the structure f Γ (for an elastic body found from the local stresses, for a solid body found from their integration along the interface).…”