Finite volume method with Walsh basis function (FVM–WBF) is a novel high-resolution method capable of capturing discontinuities effectively within the cell [1]. In this method, the conservative variables within each cell are expanded in a series of Walsh functions with inherent discontinuous characteristics, yielding a piecewise-continuous description over sub-cells inside a control volume and thus breaking the conventional assumption of a continuous in-cell distribution. By increasing the number of basis functions, the in-cell numerical resolution can be significantly enhanced. Existing studies have thoroughly validated the excellent shock-capturing performance of FVM–WBF for inviscid flows; however, its potential for resolving complex viscous flows containing multi-scale structures still requires further in-depth investigation. To systematically assess the method’s performance for such complex flows, three-dimensional supersonic open-cavity flow is selected as a test case [2-3]. This flow not only exhibits self-sustained oscillations driven by the nonlinear feedback between the shear layer and acoustic waves, but also contains shock waves and multiscale vortex/turbulent structures within the flow field, thereby imposing higher demands on the numerical method’s local resolution and discontinuity-capturing capabilities. The numerical results indicate that, as the order of the Walsh basis functions increases, the ability to resolve shocks and small-scale turbulent vortical structures is significantly enhanced. This further confirms that the FVM-WBF method not only provides robust discontinuity-capturing performance, but also demonstrates great potential for high-fidelity simulations of complex unsteady flows.