A configurable application for simulation of backward-facing step problem
The aim of this tutorial is to show how to build and solve the backward-facing step model using lattice Boltzmann method in waLBerla. The "01_BasicLBM" case is used as the foundation of the current work. Therefore, most of the functionalities have already been introduced and discussed in LBM 1 tutorial. Here the main focus is on the following areas:
A 2D channel flow with a backward-facing step is simulated. The application is configured with the Reynolds number and lattice velocity as input and reattachment location as the output. The input parameters are specified in a configuration file while the calculation and writing of reattachment locations are performed in a functor
ReattachmentLengthFinder which is implemented inside the program.
Since the simulations are carried out in 2D, the standard D2Q9 stencil with SRT collision model is used which is already implemented in the 'lbm' module.
The main() function must be modified so that the program could accept the Reynolds number and lattice velocity as input parameters. These parameters are specified in the 'parameters' section of the config file.
The following lines inside the main() function reads these two values from the parameters section of the configuration file:
The height of the channel is considered as the reference length in this simulation (it may differ in other applications). This value is read from the DomainSetup section in the configuration file where the dimensions of the channel are specified.
Finally, viscosity consequently omega are calculated with the Reynolds number, lattice velocity and reference length.
Since the step geometry is a plain rectangular area, the simplest approach is to create it by geometry module in walberla. This module offers capability to read boundaries of a random geometry from images, voxel files, coordinates of vertices, etc. Using this module, obstacles of basic shapes could be conveniently positioned inside the domain. It is also easier to have the program to read the geometry specifications from the Boundaries section of the configuration file. This is implemented by reading and storing the Boundaries block of the configuration file in 'boundariesConfig' object and passing it to a convenience function provided in the geometry class to initialize the boundaries.
Here a subblock 'Body' is created inside 'Boundaries' section in the configuration file in order to create a box (rectangle in 2D) using two diagonal vertices.
For more details about specifying boundaries using configuration file, please refer to the documentation of walberla::geometry::initBoundaryHandling().
In order to find the reattachment location precisely, the velocity on each lattice cell on the bottom boundary line of the domain following the step is examined. The idea is to locate the exact position on the bottom boundary in which the streamwise velocity component switches sign. This mechanism is implemented by a functor named
ReattachmentLengthFinder and is passed to a method of timeloop 'addFuncBeforeTimeStep()'' to create the logger.
After running the program, the locations of reattachment against timestep are written to 'ReattachmentLengthLogging_Re_[Re].txt' in the working directory. Note that there might be more than one reattachment location before the flow fully develops along the channel, and all are given in the file. This simply means that it is expected to have multiple occurences of seperation and reattachment at the same time along the bottom boundary of the channel following the step in the early stages. However, most of them are smeared later as the flow starts to develop. The logging frequency can also be adjusted by 'checkFrequency' which is passed to the
The following results of the normalized reattachment length were obtained by a numerical study, using the here developed application. Note that it might take a long time until the simulation has reached a steady state and the final values for this length can be obtained. Also, the step has to be long enough to feature a converged, parabolic flow profile before the expansion, and the domain itself has to be long enough to not perturb the results by the vicinity of the outflow boundary condition. Reference results were taken from Ercan Erturk, “Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions”, Computers & Fluids, Vol. 37, 2008.
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To improve this application, parallelization with a proper synchronization of the reattachment lengths could be added. Also, a stopping criterion based on the convergence of some relevant quantity could be added to avoid a manual termination of the simulation.