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

Abstract

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

Discrete Energy-Conservation Properties in the Numerical Simulation of the Navier–Stokes Equations

“…The group of Oliva and coworkers has applied the symmetry-preserving unstructured method developed by Trias et al [53] to study complex flows over a car model [111,112], a NACA0012 in full stall [113], and a circular cylinder [114]. Rozema et al [115] investigated the flow over a delta wing using a fourth-order symmetry-preserving scheme for compressible flow derived in the framework of the square-root formulation [48] (cf. Sec.…”

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

“…Previously, the energy-conserving simulation method for compressible flow has been used for large-eddy simulation of the flow over a delta wing, yet at a slightly smaller Reynolds number [55]. These simulations were numerically stable and gave physically accurate results.…”