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The recently proposed high-order TENO scheme [Fu et al., Journal ofComputational Physics, 305, pp.333-359] has shown great potential in predictingcomplex fluids owing to the novel weighting strategy, which ensures thehigh-order accuracy, the low numerical dissipation, and the sharpshock-capturing capability. However, the applications are still restricted tosimple geometries with Cartesian or curvilinear meshes. In this work, a newclass of high-order shock-capturing TENO schemes for unstructured meshes areproposed. Similar to the standard TENO schemes and some variants of WENOschemes, the candidate stencils include one large stencil and several smallthird-order stencils. Following a strong scale-separation procedure, a tailorednovel ENO-like stencil selection strategy is proposed such that the high-orderaccuracy is restored in smooth regions by selecting the candidatereconstruction on the large stencil while the ENO property is enforced neardiscontinuities by adopting the candidate reconstruction from smooth smallstencils. The nonsmooth stencils containing genuine discontinuities areexplicitly excluded from the final reconstruction, leading to excellentnumerical stability. Different from the WENO concept, such unique sharp stencilselection retains the low numerical dissipation without sacrificing theshock-capturing capability. The newly proposed framework enables arbitrarilyhigh-order TENO reconstructions on unstructured meshes. For conceptualverification, the TENO schemes with third- to sixth-order accuracy areconstructed. Without parameter tuning case by case, the performance of theproposed TENO schemes is demonstrated by examining a set of benchmark caseswith broadband flow length scales.

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