Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows

“…The following test case consists of the convection of a 2D compressible vortex in a periodic domain so as to accumulate numerical errors from the discretization schemes. This test case exhibits a smooth solution and weak compressibility effects, which allows numerical schemes to perform near their asymptotic limit 11,2 . Simulations are performed with increasing mesh resolution and the time-step is computed based on the mesh resolution via a constraint on the CFL number, set to 0.7.…”

“…Both fifth-and seventhorder schemes are able to capture the overall correct shape of the wave, and the latter one provides a better estimation of the amplitude. In the interest of clarity, the solution for this mesh size with the fourth-order finite volume method has been omitted but can be found in our previous work 2 . It is emphasized that such a solution is similar to the one computed with the hybrid PPM/WENO and the fifth-order WENO-Z scheme (blue curve in figure 2b).…”

“…The present test case consists on the simulation of the decay of a compressible isotropic turbulent field with the presence of eddy shocklets. Originally a physical study of turbulence in the work of Lee et al 12 , this framework of simulations has been employed in 13,2 to study the properties of numerical schemes to capture turbulence spectra and the decay of physical quantities. The simulation is controlled by two non-dimensional parameters: the turbulent Mach number…”

“…The study presented in 2 shows that for a problem involving a smooth solution, the high-order method performs better than the second-order ones and that the theoretical order of convergence rate is retrieved. However, when the solution contains a shock all the methods collapse to a first-order convergence rate.…”

“…The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces and to assess their interaction with the volume integration method. The present study takes advantage of the hybrid PPM/WENO strategy that has been developed in 2 . Whereas the whole integration scheme is a second-order Godunov method with PPM interpolation, the reconstruction of data at cell faces can be performed by any WENO scheme.…”