Accession Number:

ADA626097

Title:

Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations

Descriptive Note:

Technical paper Jun-Jul 2015

Corporate Author:

AIR FORCE RESEARCH LAB EDWARDS AFB CA AEROSPACE SYSTEMS DIRECTORATE

Report Date:

2015-06-01

Pagination or Media Count:

0.0

Abstract:

Numerical discretization for unsteady flow simulations can be broken down into spatial and temporal parts which interplay in complex and sometimes unexpected ways. This paper attempts to address how the properties of the spatial discretization help drive the choice of temporal discretization. In addition, it examines methods for higher than second-order accurate time integration using L-stable singly-diagonally-implicit ESDIRK Runge-Kutta methods. Von Neumann analysis is used to examine the theoretical effects of different spatialtemporal discretization combinations. The predictive nature of the von Neumann analysis is then validated through the exploration of the convection of acoustic waves in one dimension and an isentropic vortex in three dimensions. Is is shown that the computational results follow the expected trends taking the von Neumann analysis of the schemes into account. This work highlights that, for unsteady problems, both dissipation and dispersion errors must be accounted for when selecting optimal Runge-Kutta time integrators.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE