Computation of Two-Dimensional Disturbances in an Elastic Body - A.A. Aganin; N.A. Khismatullina (Учёные записки Казанского университета: Серия Физико-математические науки)
The classical Godunov method is widely used for the numerical study of waves in continuous media. If the Courant condition is satisfied, the Godunov scheme is stable and monotonous. However, due to its first order of accuracy it can lead to rather large smearing of jumps, contact discontinuities, and other features of the solution in the domains where the solution gradients are great.