DEVELOPMENT OF A SOLVER FOR THE COMPRESSIBLE LARGE EDDY SIMULATIONS

Date

2023-7-26

Author

Akdemir, Mustafa

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Modelling of turbulent flows is the most challenging subject for computational engineers. Analytical solutions for the Navier-Stokes equations are non-existent, therefore the use of numerical methods is the only way to predict flows without resorting to experiments. When dealing with turbulent flows, there are three main approaches: Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). Among these, DNS stands out as the most accurate method for simulating turbulent flow due to its ability to resolve all scales in both the spatial and temporal domains. However, the computational cost of DNS, stemming from the requirement for very fine grids to capture all scales, renders it unfeasible, particularly for industrial applications. Consequently, RANS and LES have gained popularity as alternative approaches for turbulent flows. RANS, being more cost-effective, necessitates the modeling of dynamics for all scales, although certain phenomena cannot be inherently modelled. LES holds a distinct advantage over RANS in that it inherently resolves large-scale dynamics, obviating the need for their explicit modeling. However, the numerical methods employed in LES must exhibit low-dissipative properties. In this study, a novel approach to LES is pursued, aiming to develop a low-dissipative solver capable of simulating flows featuring discontinuities or shocks. This is achieved by blending a non-dissipative scheme with a dissipative scheme with the help of a shock capturing method. The non-dissipative method utilizes a central scheme that conserves kinetic energy and entropy. As for the dissipative solver, the HLLC flux calculation method, along with the Weighted Average Flux (WAF) approach, is adopted. To enhance the accuracy of the dissipative scheme, the Multi-Slope MUSCL reconstruction method is employed to compute the flow variables on the faces. Time integration is carried out using the strong stability-preserving third-order total diminishing Runge-Kutta discretization method. While LES can resolve large-scale dynamics, the small-scale dynamics still necessitate modeling, as is the case in RANS. To tackle these sub-grid level phenomena, the compressible Smagorinsky model with a constant coefficient is utilized.

Subject Keywords

Tubulence, Large-Eddy Simulation, Compressible Solver, Low-Dissipation

URI

https://hdl.handle.net/11511/105223

Collections

Graduate School of Natural and Applied Sciences, Thesis