A stiffly-stable implicit Runge-Kutta algorithm for CFD applicationsA stiffly-stable implicit Runge-Kutta integration algorithm is derived for CFD applications spanning the range of semidiscrete theories. The algorithm family contains the one-step 'theta' algorithms, including backwards Euler and the trapezoidal rule, and provides a versatile framework to identify expressions governing algorithm stability characteristics. Parameters of a Runge-Kutta optimal implicit algorithm, second-order accurate in time and stiffly-stable, are established. This algorithm is implemented within a weak statement finite element semidiscrete formulation for one- and two-dimensional conservation law systems. Numerical results are compared to theta-algorithm solutions, for unsteady quasi-one-dimensional Euler predictions with shocks, and for a specially derived two-dimensional conservation law system modeling the Euler equations.
Document ID
19880035081
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Baker, A. J. (Tennessee, University Knoxville, United States)
Iannelli, G. S. (Tennessee Univ. Knoxville, TN, United States)