PRACTICAL ASPECTS OF SPATIALLY HIGH-ORDER ACCURATE METHODS

The computational qualities of spatially high-order accurate methods for the finite-volume solution of the Euler equations are presented. Multidimensional reconstruction operators discussed include versions of the k-exact and essentially nonoscillatory (ENO) algorithms. The ENO schemes utilized are the reconstruction-via-primitive-function scheme and a dimensionally split ENO reconstruction. High-order operators are compared in terms of reconstruction and solution accuracy, computational cost, and oscillatory behavior in supersonic flows with shocks. Inherent steady-state convergence difficulties are demonstrated for the implemented adaptive-stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected through operation counts. The standard variable-extrapolation method (MUSCL) is included for comparison. Numerical experiments include the Ringleb flow for numerical accuracy and a shock-reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.