High-order finite-volume central targeted essentially non-oscillatory schemes for shock-driven flows on unstructured meshes

Abstract The high-order targeted essentially non-oscillatory (TENO) scheme, known for its innovative weighting strategy, has demonstrated strong potential for complex flow predictions and applications. This study extends the TENO weighting approach to develop a family of central TENO (CTENO) schemes for unstructured meshes. The CTENO schemes employ compact directional stencils, which increase the likelihood of finding all stencils within smooth regions. The design is intentionally compact to simplify the implementation of directional stencils. An effective scale-separation strategy is adopted via an essentially non-oscillatory (ENO)-like stencil selection method, which employs large central stencils in smooth areas to achieve high-order accuracy, and employs smaller directional stencils near discontinuities to improve shock-capturing capability. Extensive tests involving central weighted essentially non-oscillatory (CWENO), TENO, and CTENO family schemes are conducted to assess their performance in terms of accuracy, parallel scalability, and computational efficiency. The applications to shock-driven flows indicate that the proposed schemes deliver high-order accuracy, lower numerical dissipation, and excellent shock-capturing performance in several practical flow cases such as shock reflection, bubble dynamics, explosion, and particle flow problems.