On the approximation of dam-break problems using a fuzzified HR-TVD scheme

Abstract

The construction of the proposed second-order accurate scheme is based on the Monotonic Upstream Schemes for Conservation Laws (MUSCL) strategy. Using some strong notions from fuzzy logic, like fuzzy modifiers and fuzzy inference systems, the work offers a new avenue for optimizing the execution of classical flux-limiting algorithms. A numerical study has also been included to compare the new limiting scheme and the classical Monotonized Central (MC) scheme. The key themes of the research work are:•Development of the background theory and augmented Riemann finite volume (FV) framework required to construct the new fuzzy logic-based limiter for the Shallow Water Equations (SWEs) over flat bottom topography.•The proposed fuzzy flux limiting technique has been employed in a structured one-dimensional FV model to compute the SWEs.•The idealized dam-break flows verify the new fuzzified High-Resolution (HR), Total Variation Diminishing (TVD) technique.