PRACTICAL ASPECTS OF SPATIALLY HIGH-ORDER ACCURATE METHODS

The computational qualities of spatially high-order accurate methods f or the finite-volume solution of the Euler equations are presented. Mu ltidimensional reconstruction operators discussed include versions of the k-exact and essentially nonoscillatory (ENO) algorithms. The ENO s chemes utilized are the reconstruction-via-primitive-function scheme a nd a dimensionally split ENO reconstruction. High-order operators are compared in terms of reconstruction and solution accuracy, computation al cost, and oscillatory behavior in supersonic flows with shocks. Inh erent steady-state convergence difficulties are demonstrated for the i mplemented adaptive-stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computatio nal intensity is reflected through operation counts. The standard vari able-extrapolation method (MUSCL) is included for comparison. Numerica l experiments include the Ringleb flow for numerical accuracy and a sh ock-reflection problem. A vortex-shock interaction demonstrates the ab ility of the ENO scheme to excel in simulating unsteady high-frequency flow physics.