Compact-Corrected MUSCL: A Flexible, Low-Cost High-Accuracy Scheme for High-Speed Flow Simulation

High-order numerical methods are essential for achieving predictive fidelity in modern computational fluid dynamics, yet many existing schemes face significant trade-offs between accuracy, robustness, and computational efficiency. This study introduces the Compact-Corrected MUSCL (CCMUSCL) scheme, a novel framework that enhances the traditional MUSCL approach by incorporating localized information from high-order, compact finite-difference formulas. Unlike classical compact schemes that require solving global linear systems, this method applies corrections locally to the MUSCL flux. This strategy allows the scheme to maintain spectral-like resolution while preserving the robustness and locality of the original MUSCL framework. The performance of CCMUSCL is evaluated using a series of rigorous 1D and 2D benchmark cases. Numerical results demonstrate that CCMUSCL achieves accuracy comparable to or exceeding that of traditional high-order WENO schemes, particularly in resolving intricate, small-scale flow structures and sharp discontinuities. Furthermore, efficiency analysis reveals that CCMUSCL is significantly more cost-effective than WENO, requiring substantially fewer arithmetic operations in 1D and offering an even more pronounced reduction in operations for 3D flux evaluations. By offering a tunable balance between robustness and accuracy through the use of the van Albada limiter as a localized indicator, the CCMUSCL scheme provides a highly efficient and flexible alternative for large-scale high-speed flow simulations.