This article presents a formulation that extends the variational multiscale modelling for compressible large-eddy simulation to a vast family of compact nodal numerical methods represented by the high-order flux reconstruction scheme. The theoretical aspects of the proposed formulation are laid down via rigorous mathematical derivations which clearly expose the underlying assumptions and approximations and provide sufficient details for accurate reproduction of the methodology. The final form is assessed on a Taylor-Green vortex benchmark with Reynolds number of 5000 and compared to filtered direct numerical simulation data. These numerical experiments exhibit the important role of sufficient de-aliasing, appropriate amount of upwinding from Roe's numerical flux and large/small scale partition, in achieving better agreement with reference data, especially on coarse grids, when compared to the baseline implicit large-eddy simulation.
This work is concerned with the development of a framework for the efficient design of cooling channels via two different topology optimization paradigms: a diffuse and a sharp. Each approach relies on a distinct thermo-fluid modeling and features a specific material distribution mode, i.e. fraction-based (diffuse) versus interface-based (sharp). The two models are described and the corresponding solvers are validated. A gradient-based optimization methodology is adopted and the details of the adjoint-based gradient computation are introduced. Finally, examples of cooling channel design optimization are presented and discussed.
The objective of this work is to compare two topology optimization strategies, i.e. density-based (diffuse) and level-set-based (sharp), in thermal problems involving a heat conductor and an insulation material. The fundamental difference between the two methods lies in the representation of the materials’ interface: the density method allows for transitional regions whereas the level set one does not. Several regularization techniques, such as perimeter restriction, parameter ramping, level set gradient restriction and parametrization, are explored in order to enhance each method’s robustness and to decrease its sensitivity to initial conditions. It is shown that, in the two test problems investigated, the diffuse method was in general more robust than the sharp one. However, when combined with appropriate regularization techniques, the level set method lead to material distributions which were more optimal.
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