ABSTRACT
Numerically it may be difficult to determine when the residual (or viscosity) is of order D..x-1. This difficulty may usually be overcome by computing the numerical solution on two grids with different spatial spacings D..x1 and D..x2. Let R1 and R2 be approximations to the residuals of the solutions on these meshes. When the ratio Rl/ R2 of the residuals is within some tolerance of D..x2 f D..xb then we treat the region as being inside a shock (or shock layer). It should be mentioned that asymptotic analysis and numerical experiments show under general conditions that strong singularities are not well localized by any approximation of the gradient of the solution.
