A generalized ENO reconstruction in compact GKS for compressible flow simulations

TL;DR

This paper introduces a generalized ENO reconstruction method that enhances high-order compressible flow simulations by improving accuracy, robustness, and shock-capturing capabilities, especially when integrated with compact GKS schemes.

Contribution

It develops a simplified, adaptive GENO reconstruction scheme that seamlessly combines high-order linear and nonlinear reconstructions for unstructured meshes.

Findings

Demonstrates superior accuracy over existing WENO methods.

Shows robustness and shock-capturing in benchmark tests.

Validates effectiveness within high-order compact GKS.

Abstract

This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory behavior at discontinuities. By generalizing the adaptive philosophy of ENO schemes, the method employs a smooth path function that directly connects high-order linear reconstruction with a reliable lower-order alternative. This direct adaptive approach significantly simplifies the construction of nonlinear schemes, particularly for very high-order methods on unstructured meshes. A comparative analysis with various WENO methods demonstrates the reliability and accuracy of the proposed reconstruction, which provides an optimal transition between linear and nonlinear reconstructions across all limiting cases based on stencil smoothness. The consistency and performance of the GENO reconstruction are validated through implementation in both high-order compact gas-kinetic schemes (GKS) and non-compact Riemann-solver-based methods. Benchmark tests confirm the robustness and shock-capturing capabilities of GENO, with particularly superior performance when integrated with compact schemes. This work advances the construction methodology of nonlinear schemes and establishes ENO-type reconstruction as a mature and practical approach for engineering applications.