Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:433402

Lorber, A A; Carey, G F; Bova, S W; Harle, C H ^[1]

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1. Univ. of Texas, Austin, TX (United States)

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

• Research Organization: Front Range Scientific Computations, Inc., Lakewood, CO (United States)
• OSTI ID: 433402
• Report Number(s): CONF-9604167--Vol.1; ON: DE96015306
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
CONVECTION
CONVERGENCE
DIFFUSION
FLUID FLOW
FUNCTIONS
HYPERSONIC FLOW
ITERATIVE METHODS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
POLYNOMIALS
VISCOUS FLOW