scholarly journals Time integration schemes for the unsteady Navier-Stokes equations

2001 ◽  
Author(s):  
Hester Bijl ◽  
Mark Carpenter ◽  
Veer Vatsa
Keyword(s):  
Stokes Equations ◽  
Time Integration ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Integration Schemes ◽  
Time Integration Schemes

scholarly journals A Navier-Stokes Inverse Method Based on a Moving Blade Wall Strategy

1997 ◽  
Author(s):  
Olivier Léonard ◽  
Alain Demeulenaere
Keyword(s):  
Inverse Method ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Time Integration ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
The Difference ◽  
Compressor And Turbine Blades

A two-dimensional viscous inverse method for the design of compressor and turbine blades is presented. An initial geometry is modified iteratively to reach a target pressure distribution imposed on the blade surfaces. The Navier-Stokes equations are solved in a numerical domain of which some boundaries (the blade walls) move during the transient part of the computation. The blade modifications are based on the transpiration principle. The transpiration flux is computed from the difference between the actual and the prescribed pressure distributions. A high-resolution Navier-Stokes solver has been developed for this purpose, based on a Finite-Volume formulation. Multi-block structured grids allow for a selective concentration of discretization points in the zones of higher gradients. Both explicit (Runge-Kutta) and implicit (Newton-Krylov) time integration schemes have been implemented. Applications to turbine and compressor blade design illustrate the accuracy of the flow computation, and the efficiency of the inverse method.

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