Weighted Essentially Non-Oscillatory Schemes - Survey and Recent Developments

Explore the fundamentals and cutting-edge advancements in Weighted Essentially Non-Oscillatory (WENO) schemes through this comprehensive conference talk delivered by Chi-Wang Shu at the International Conference on Boundary and Interior Layers (ICBS2025), hosted by BIMSA. Gain insights into the theoretical foundations of WENO schemes, which are high-order accurate numerical methods designed to capture sharp gradients and discontinuities in solutions of hyperbolic partial differential equations without spurious oscillations. Discover the latest developments in this field, including improvements to the original WENO methodology, enhanced efficiency techniques, and novel applications across various computational fluid dynamics problems. Learn about the mathematical principles underlying these schemes, their implementation strategies, and how recent research has addressed challenges in maintaining high-order accuracy while preserving stability near discontinuities. Understand the practical applications of WENO schemes in solving complex problems involving shock waves, contact discontinuities, and other challenging phenomena in computational mathematics and engineering.