FiniteDifference Calculations for Hydrodynamic Flows Containing Discontinuities
Abstract
In this paper it is shown how to calculate the steady hypersonic inviscid flow, including a detached shock, around a blunt body. The steady flow is obtained as the limit for large time of timedependent flow, starting with plane flow impinging on the body. The transient flow is the solution of a mixed initialboundaryvalue problem for the partial differential equations of inviscid fluids which is solved by a difference scheme proposed by Lax and Wendroff. Our calculations show that by itself this difference scheme tends to be unstable and does not converge to the steady flow; by adding an artificial viscosity term we have succeeded in stabilizing the calculation. Section 4 is a fairly convincing theoretical explanation of this stabilizing effect and a new stability condition is derived. Both plane and cylindrical symmetries are considered; in the cylindrical case a variant of Richtmyer's [4] twostep version of the LaxWendroff difference scheme is used. This method, as does Richtmyer's, requires much fewer arithmetic operations as compared with the onestep method.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 1966
 DOI:
 10.1016/00219991(66)900039
 Bibcode:
 1966JCoPh...1..198B