Kernkonzepte
The author presents an alternative finite difference WENO scheme for hyperbolic systems with non-conservative products, aiming to achieve exact conservation and high-order accuracy.
Zusammenfassung
The content discusses the development of efficient alternative finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for hyperbolic systems with non-conservative products. It introduces the classical finite difference WENO method and the newer alternative finite difference WENO (AFD-WENO) method. The AFD-WENO algorithm is designed to handle hyperbolic systems with non-conservative products efficiently while maintaining high accuracy. The paper demonstrates that AFD-WENO outperforms FD-WENO in terms of speed and cost-effectiveness, especially in Peta- and Exascale computing scenarios. By transitioning to a precise conservation form when non-conservative products are absent, shock locations can be accurately captured by the method. The formulation presented allows flexibility in using different Riemann solvers and performs well on problems with stiff source terms. Various test problems are discussed to showcase the effectiveness of AFD-WENO for hyperbolic systems.
Statistiken
Higher order variants of AFD-WENO schemes don’t cost much more than lower order variants.
AFD-WENO outperforms FD-WENO at all orders.
The larger number of floating point operations associated with larger stencils are efficiently amortized by the CPU when designed to be cache friendly.