Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
A new Direct Numerical Simulation code of boundary layer flows verified by the method of manufactured solutions
Submission Author:
Mateus Ribeiro , SP
Co-Authors:
Mateus Ribeiro, Livia S. Freire, Leandro Franco de Souza
Presenter: Mateus Ribeiro
doi://10.26678/ABCM.COBEM2021.COB2021-0845
Abstract
Turbulent flows have been widely studied due to their presence in many phenomena in nature and industry. Because of the lack of analytical solution of the governing equations, the study of turbulence depends on the development of numerical simulations among its main tools. There are currently several techniques for turbulent flow simulation, including Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). DNS numerically solves the governing equations and captures all scales of the turbulent flow, which guarantees a high reliability of the results, but at a high computational cost. On the other hand, LES solves only the largest scales of the problem, taking the effects of the smallest scales into account by using a subgrid scale model. LES stands out for having adequate computational cost for the simulation of some large-scale and highly turbulent applications, such as the atmospheric boundary layer (ABL). Thus, it is evident the importance of testing different methodologies and techniques that can be used in the development of efficient DNS and LES codes, which include different formulations of the budget equations, the use of different techniques for approximating spatial and temporal derivatives, the organization of the grid, among others. The objective of this work is to develop an efficient DNS code with great potential for simulating turbulence in three-dimensional and incompressible boundary layer flows, which can be verified with consolidated theories and data from the literature. A velocity-vorticity formulation was chosen to solve the Navier-Stokes equations, which allows to eliminate the flow pressure term. In addition, periodic conditions were adopted in the longitudinal and transverse directions. Therefore, it was possible to use the spectral method for the calculation of spatial derivatives in these directions, providing exact solutions and reducing numerical errors. In the vertical direction, a stretched grid method was used to obtain better precision in the region close to the wall, and a high-order compact finite difference method was used to calculate the spatial derivatives. The time derivative is integrated by a fourth order Runge-Kutta method and the code was verified by the method of manufactured solutions (MMS), which forces a known solution by choosing the boundary conditions and by adding source terms to the original set of equations. An efficient DNS code was obtained for turbulent, three-dimensional and incompressible boundary layer flows. In the future, this code will be adapted to the LES methodology, in order to simulate the ABL.
Keywords
Boundary layer flow, High-order compact finite-difference scheme, Verification, Method of Manufactured Solutions, Spectral Method, direct numerical simulation
