Summary of Solutions to Category 1, Problem 3

The goal of this problem was to provide a detailed study of the accuracy of boundary treatments with a range of incidence angles including shear and a sonic point. There are three parts. In each we solve the linearized Euler equations on a prescribed domain: (-2, 2) x (0, 1) with initial conditions consisting of a pressure dipole, entropy and vorticity disturbances. Here x1 =
±2 are the artificial boundaries, the speed of sound is scaled to 1, and we solve up to t = 64. The solvers were asked to provide l2 relative errors computed on a 129 x 33 mesh at 18 time stations ranging from 1 to 64. We note that these problems present a very stringent test of the boundary treatments, as at later times waves are incident on the arti.cial boundaries at increasingly skew angles. We also note that in many settings it might be more appropriate to measure the errors relative to the size of the initial disturbance, rather than against the solution remaining in the computational domain. Then the O(100%) late time relative errors reported below by some solvers are O(1% - 20%), which may be acceptable.