Higher Order Central Schemes for Multi-dimensional Hyperbolic Problems
For researchers in computational fluid dynamics and hyperbolic PDEs, this work offers an incremental improvement in accuracy and efficiency over existing CWENO-based central schemes.
The paper develops a fourth-order central scheme for multi-dimensional hyperbolic problems using an efficient dimension-by-dimension CWENO reconstruction, demonstrating fourth-order accuracy and shock capturing in nonlinear problems, with reduced numerical dissipation and computational cost compared to third-order implementations.
Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and shock capturing nature of the scheme are demonstrated in various nonlinear multi-dimensional problems. In order to show the overall performance of the present central scheme numerical errors and non-oscillatory behavior are compared with existing multi-dimensional CWENO based central schemes for various multi-dimensional problems. Moreover, the benefits of the present fourth order central scheme over third order implementation are shown by comparing the numerical dissipation and computational cost between the two.