A Code for Simulating Heat Transfer in Turbulent Channel Flow

Abstract

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

A deep-learning approach for reconstructing 3D turbulent flows from 2D observation data

“…DNS calculations of a fully-developed incompressible turbulent channel flow at friction Reynolds numbers and 500 are performed to generate the training and testing datasets. The incompressible Navier–stokes equations are solved using the LISO code 48 , similar to the one described by Lluesma-Rodriguez et al 63 . This code has successfully been employed to run some of the largest simulations of wall-bounded turbulent flows 52 , 64 , 65 .…”

“…The 2D3DGAN is trained separately with the data of turbulent channel flow at Re τ = u τ δ/ν = 180 and 500, and with the data of flow around a finite wall-mounted square cylinder with AR = 4, and at Re d = U ∞ d/ν = 500 , where, δ is the channel half-width. For the case of turbulent channel flow, the transfer-learning technique 16,22,29 48 , similar to the one described by Lluesma-Rodriguez et al 63 . This code has successfully been employed to run some of the largest simulations of wall-bounded turbulent flows 52,64,65 .…”

Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives

“…Note that in the following x, y, and z are the streamwise, wall-normal and spanwise components, respectively. These equations can be transformed for simple domains [21,22] into the vorticity-Laplacian form, see also [23]. In such geometries, one can take advantage of the derived formulation in the y component of the vorticity ω y , and the bi-Laplacian of the wall-normal velocity Φ, as explained in Ref.…”

“…where h v and h g collect the nonlinear part of the Equations ( 1) and (2) [22]. For instance, in turbulent channel flow, there are two periodic directions that allow the use of fast-Fourier methods in these directions.…”

“…For instance, in turbulent channel flow, there are two periodic directions that allow the use of fast-Fourier methods in these directions. This method was used in the first large DNS of wall turbulence [21], and in many more after that [5,22,24]. Using Fourier methods, instead of solving one large equation one has to solve millions of one-dimensional (1D) equations.…”