High-order Finite-Volume Central Targeted ENO Family Scheme for Compressible Flows in Unstructured Meshes

TL;DR

This paper introduces high-order non-oscillatory central TENO schemes for unstructured meshes, enhancing accuracy and shock-capturing in compressible flow simulations through innovative stencil strategies.

Contribution

It extends the TENO scheme to develop compact, high-order central schemes (CTENO and CTENOZ) with improved shock-capturing and implementation simplicity for unstructured meshes.

Findings

High-order accuracy achieved with CTENO schemes.

Enhanced shock-capturing capabilities demonstrated.

Good parallel scalability and computational efficiency.

Abstract

The high-order Target ENO (TENO) scheme, known for its innovative weighting strategy, has demonstrated strong potential for complex flow predictions. This study extends the TENO weighting approach to develop non-oscillatory central TENO (CTENO and CTENOZ) family schemes for unstructured meshes. The CTENO schemes employ compact directional stencils, which increase the likelihood of finding stencils within smooth regions. The design is intentionally compact to simplify the implementation of directional stencils. An effective scale separation strategy is adopted using an ENO-like stencil selection method, which employs large central stencils in smooth regions to achieve high-order accuracy, and smaller directional stencils near discontinuities to improve shock-capturing capabilities. Extensive tests involving CWENO, TENO, CTENO, and CTENOZ schemes were conducted to assess their performance in terms of accuracy, robustness, parallel scalability, and computational efficiency. The findings indicate that the proposed CTENO and CTENOZ schemes deliver high-order precision, lower numerical dissipation, and excellent shock-capturing performance.