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

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Fuzzy logic applications

Background:

• Classical flux-limiting algorithms can be computationally intensive.
• Optimizing numerical schemes is crucial for accurate fluid dynamics simulations.
• Shallow Water Equations (SWEs) model various free-surface flows.

Purpose of the Study:

• To develop a novel fuzzy logic-based flux limiter for the Shallow Water Equations (SWEs).
• To enhance the accuracy and efficiency of numerical simulations for fluid dynamics.
• To optimize the execution of classical flux-limiting algorithms.

Main Methods:

• Development of a fuzzy logic-based limiter within an augmented Riemann finite volume (FV) framework.
• Implementation of the fuzzy flux limiting technique in a structured one-dimensional FV model.
• Utilizing fuzzy modifiers and fuzzy inference systems for algorithm optimization.

Main Results:

• A new second-order accurate scheme based on the Monotonic Upstream Schemes for Conservation Laws (MUSCL) strategy was constructed.
• The proposed fuzzy flux limiting technique was successfully employed to compute SWEs.
• Numerical studies demonstrated the effectiveness of the new fuzzified High-Resolution (HR), Total Variation Diminishing (TVD) technique.

Conclusions:

• The fuzzy logic-based flux limiter offers a new avenue for optimizing classical flux-limiting algorithms.
• The developed technique provides a more accurate and potentially efficient method for simulating SWEs.
• Idealized dam-break flows validated the performance of the new fuzzified HR, TVD technique.