A fuzzy c-means based dual-layer flux-blending framework for high-resolution dam-break simulations

Dam-break flow modelling involves a trade-off as resolving steep gradients requires high-order discretisations, yet these tend to generate spurious oscillations near discontinuities. Moreover, classical limiters used to suppress such oscillations rely largely on single-parameter algebraic indicator rules. This study replaces the procedure with a fuzzy c-means flux-blending framework for the finite-volume solution of the shallow water equations. To this end, an unsupervised classifier is trained on local hydraulic descriptors to assign each interface a shock-membership grade, and a second fuzzy inference layer converts that grade into a weight that blends a high-order flux with a dissipative low-order flux. The limiter-based transition is thereby replaced by a data-driven transition whose behaviour is determined by a measurable flow structure rather than a fixed algebraic rule. Accordingly, dissipation is graded continuously with the local flow structure. To validate the framework, one- and two-dimensional wet-bed and dry-bed dam-break benchmarks, including circular and partial-breach configurations, are considered. Against the exact Stoker and Ritter solutions, the scheme attains $$\:{L}_{1,h}$$ errors of 0.0664 and 0.0257 for the one-dimensional wet-bed and dry-bed cases, respectively, placing it between the first-order Rusanov scheme and the Minmod-TVD limiter. In the two-dimensional partial breach, the framework produces a qualitatively similar diffraction pattern to the Minmod-TVD scheme without inducing non-physical oscillations. For the configurations tested, graded and interpretable flux control provides a viable alternative to limiter-based transition.