Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
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 spatial/temporal 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 2015
- Accession Number
- ADA626097
Entities
People
- Ayaboe Edoh
- Nathan L. Mundis
- Venkateswaran Sankaran
Organizations
- Air Force Research Laboratory