Development of high order WENO schemes for large-eddy simulation of compressible flows in OpenFOAM - U S Vevek (Nanyang Technological University, 2020)
Performing LES of compressible flows is a challenging affair. On the one hand, one strives to minimize numerical dissipation to preserve ‘all’ scales of motions. On the other hand, introducing some dissipation is necessary to guarantee numerical stability near sharp gradients and to capture shocks. High order shock-capturing schemes are able to meet these contradicting demands and WENO schemes are one class of such schemes that has found great success in the past few decades. Unfortunately, most, if not all, commercial software still rely on second order methods and do not allow the incorporation of new discretization schemes. While individual research groups have developed sophisticated high order schemes, these are proprietary in-house codes. Developing an in-house code from scratch is a daunting process but the proliferation of opensource code has opened up another avenue for the development of new CFD codes. In the recent years, OpenFOAM, an opensource CFD toolkit, has been extensively used in the development of customized numerical schemes and solvers. However, the most popular of its compressible flow solvers, rhoCentralFoam, is hardly suitable for LES since it uses TVD schemes for shock-capturing which revert to being only first order accurate in non-monotone regions. Therefore, the overall aim of the present work was to implement high order WENO schemes in OpenFOAM and construct a transient compressible flow solver for performing LES of compressible flow. With this goal in mind, an arbitrary order WENO scheme capable of handling non-uniform meshes and moderate non-orthogonality has been implemented in OpenFOAM as a standalone library. The scheme is implemented in a localized, face-based manner (dimensional split approach) for efficiency and robustness. The computation of sub-stencil smoothness indictors is implemented in a general, positive semi-definite form using polynomial coefficients rather being hardcoded using explicit expressions. A transient flow solver has also been developed to run in conjunction with the WENO library. The solver employs a novel hybrid flux scheme which exploits the efficient computation of smoothness indicators to achieve significant speedups. The accuracy and efficiency of the WENO schemes and the hybrid solver have been demonstrated using suitable linear advection and Euler test cases. To reduce the numerical dissipation of the WENO schemes further, a new adaptive mapping procedure, sensitive to the local smoothness of the solution, was designed based on a new family of mapping functions g_{\text{IM+}}\left(ω; k, m, s\right). A parametric study was performed to determine suitable values of the parameters. The resultant adaptive mapped WENO scheme, referred to as WENO-AIM(4,2,1e4), has been demonstrated to outperform many existing improved WENO schemes in several benchmark test cases. Finally, the hybrid solver was used to perform large-scale LES of under-expanded supersonic jets using seventh order WENO-AIM(4,2,1e4) scheme. The results have been found to be in good agreement with experimental schlieren images and microphone measurements. In particular, the frequency and amplitude of screech tone at NPR=5 was found to match experimental results well.