Multigrid calculation of three-dimensional turbomachinery flows
Abstract
Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.
- Publication:
-
Final Report
- Pub Date:
- June 1989
- Bibcode:
- 1989corn.rept.....C
- Keywords:
-
- Alternating Direction Implicit Methods;
- Computational Fluid Dynamics;
- Computational Grids;
- Euler Equations Of Motion;
- Inviscid Flow;
- Navier-Stokes Equation;
- Rotor Blades (Turbomachinery);
- Three Dimensional Flow;
- Transonic Flow;
- Turbomachine Blades;
- Turbomachinery;
- Two Dimensional Flow;
- Airfoils;
- Algorithms;
- Cascade Flow;
- Convergence;
- Data Smoothing;
- Dissipation;
- Factorization;
- Runge-Kutta Method;
- Step Functions;
- Fluid Mechanics and Heat Transfer