A review and comparative study of upwind biased schemes for compressible flow computation. Part II: 1-D higher-order schemes

Higher-order upwind biased procedures for solving the equations of 1-D comp ressible unsteady flow are surveyed. Approaches based upon the use of eithe r switched artificial viscosity, flux-limiting or slope-limiting are consid ered and described within a unified framework. The approaches are implement ed within the context of an edge-based finite element solution algorithm, w hich represents the basis for a future multi-dimensional extension on gener al grids. The performance of the different approaches is illustrated by app lication to the solution of the shock tube problem in different flow regime s.