A class of new high-order finite-volume TENO schemes for hyperbolic conservation laws with unstructured meshes

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy, the low numerical dissipation, and the sharp shock-capturing capability. However, the applications are still restricted to simple geometries with Cartesian or curvilinear meshes. In this work, a new class of high-order shock-capturing TENO schemes for unstructured meshes are proposed. Similar to the standard TENO schemes and some variants of WENO schemes, the candidate stencils include one large stencil and several small third-order stencils. Following a strong scale-separation procedure, a tailored novel ENO-like stencil selection strategy is proposed such that the high-order accuracy is restored in smooth regions by selecting the candidate reconstruction on the large stencil while the ENO property is enforced near discontinuities by adopting the candidate reconstruction from smooth small stencils. The nonsmooth stencils containing genuine discontinuities are explicitly excluded from the final reconstruction, leading to excellent numerical stability. Different from the WENO concept, such unique sharp stencil selection retains the low numerical dissipation without sacrificing the shock-capturing capability. The newly proposed framework enables arbitrarily high-order TENO reconstructions on unstructured meshes. For conceptual verification, the TENO schemes with third- to sixth-order accuracy are constructed. Without parameter tuning case by case, the performance of the proposed TENO schemes is demonstrated by examining a set of benchmark cases with broadband flow length scales.

UCNS3D: An open-source high-order finite-volume unstructured CFD solver

UCNS3D is an open-source computational solver for compressible flows on unstructured meshes. State-of-the-art high-order methods and their associated benefits can now be implemented for industrial-scale CFD problems due to the flexibility and highly-automated generation offered by unstructured meshes. We present the governing equations of the physical models employed in UCNS3D, and the numerical framework developed for their solution. The code has been designed so that extended to other systems of equations and numerical models is straightforward. The employed methods are validated towards a series of stringent well-established test problems against experimental or analytical solutions, where the full capabilities of UCNS3D in terms of application spectrum, robustness, efficiency, and accuracy are demonstrated.

JFM Rapids paper from the lab of Prof. FU