Date of this Version
NASA Technical Memorandum 84256, June 1982
Xost first-order upstream conservative differencing methods can capture shocks quite well for one-dimensional problems. A direct application of these first-order methods to two-dimensional problems does not necessarily produce the same type of accuracy unless the shocks are locally aligned with the mesh. Harten has recently developed a second-order high-resolution explicit method for the numerical computation of weak solutions of one-dimensional hyperbolic conservation laws. The main objectives of this paper are (a) to examine the shock resolution of Harten's method for a two-dimensional shock reflection problem, (b) to study the use of a high-resolution scheme as a post-processor to an approximate steady-state solution, and (c) to construct an implicit method in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator.