Multigrid calculation of threedimensional 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 NavierStokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit timestepping 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 threedimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit RungeKutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the threedimensional Euler equations based upon lowerupper 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 threedimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynoldsaveraged NavierStokes equations for twodimensional 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;
 NavierStokes Equation;
 Rotor Blades (Turbomachinery);
 Three Dimensional Flow;
 Transonic Flow;
 Turbomachine Blades;
 Turbomachinery;
 Two Dimensional Flow;
 Airfoils;
 Algorithms;
 Cascade Flow;
 Convergence;
 Data Smoothing;
 Dissipation;
 Factorization;
 RungeKutta Method;
 Step Functions;
 Fluid Mechanics and Heat Transfer