Adaptive Harmonic Balance Solutions to Euler's Equation

Abstract

A new adaptive harmonic balance method is presented and applied to a variety of subsonic and supersonic onedimensional e owe elds containing strong moving shocks. The adaptive method augments the frequency content in each cell as required to capture the local e ow physics. Augmentation automatically adjusts with grid density, resulting in lower frequency content on coarse grids that cannot adequately resolve high-frequency terms. A study of the effect of augmentation thresholds, increments, and scheduling on the performance and accuracy of the adaptive method is presented, and optimal parameters identie ed. When optimal parameters are used, the new adaptive harmonic balancemethod produces solutions equivalent to a nonadapted harmonic balance solution, but with up to a 50% reduction in run time.