TVD and ENO Schemes for Multidimensional Steady and Unsteady Flows A Comparative Analysis

This work deals with numerical solution of first order hyperbolic equation or system in 2D or 3D. In the first part, the solution of a 2D linear scalar equation is investigated. Using this model problem, the results of different numerical schemes are compared from the point of view of accuracy and parallel efficiency. The next part describes 2D and 3D steady numerical solutions of the transonic flow through a channel and a turbine or compressor cascade by several second order TVD methods on structured quadrilateral grids. The full TVD MacCormack and Causon’s simplified version are used and an improved version is proposed. In the last part, the numerical simulation by ENO schemes of the unsteady interaction of a shock wave with a flow inhomogeneity described by Euler or Navier-Stokes equations is presented.