Efficient Near-wall Domain Decomposition Methods for Wall-bounded Turbulent Flows

Abstract

Near-wall turbulence modeling leads to a challenging problem, as there is a thin sublayer in the vicinity of the wall that requires very fine meshes and costs the most computational time. The near-wall non-overlapping domain decomposition (NDD) method has been proven to be robust and efficient for turbulence modeling. With the NDD approach, the calculation of near-wall domains with high gradients can be excluded through transferring the wall boundary condition to an interface boundary. Meanwhile, in the approximate NDD method, the inner region near the wall can be substantially simplified using a thin-layer model and prescribed turbulent viscosity. To further improve the accuracy of the near-wall region, exact NDD without the simplifications of inner governing equations has been developed for comparison. Both approximate and exact NDD methods are explicit NDD methods that certainly require splitting the entire computational domain into two subdomains, i.e., inner region and outer region. To avoid the explicit decomposition, the implicit NDD is proposed to make future extension and implementation more straightforward. In this thesis, various near-wall domain decomposition methods are implemented into the open-source code, OpenFOAM. Code development includes a novel multi-region solver and its incorporation with the new Robin-type boundary conditions to enable the calculation of the multi-domains through the information exchanged inside the interface boundary. This thesis outlines work conducted to implement approximate NDD (ANDD) for the low-Reynolds-number (LRN) k − ε turbulence model and tested on the fully developed channel flow case. The interface boundary conditions (IBCs) for velocity and turbulent kinetic energy in the ANDD algorithm are derived based on the thin-layer model and prescribed turbulent viscosity profile in the inner region. More accuracy of the inner region resolution is compulsory for the later large eddy simulation (LES) extension. Therefore, an exact NDD (ENDD) applied to the original Reynolds-averaged Navier-Stokes equations (RANS) without any simplifications near the wall is further performed within the framework of OpenFOAM. In the manner of ENDD, the interface boundary condition for turbulent dissipation is formulated in the LRN form, following a similar procedure of the turbulent kinetic energy. Subsequently, the results of test cases with varied interface positions are analyzed in detail. Compared with ANDD predictions, the implemented ENDD method can generate better results with smooth profiles and relative insensitivity to the interface location. Furthermore, the implicit NDD (INDD) method is derived following a novel scheme to impose a Robin-type slip boundary condition at the wall, and it is demonstrated on the same channel flows with good accuracy compared to the one-block LRN solutions. More importantly, the INDD can be deployed without the explicit split of the computational domain, which significantly simplifies the implementation of NDD.

Date of Award	30 May 2024
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Sergey Utyuzhnikov (Main Supervisor) & Dominique Laurence (Co Supervisor)