The Role of Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations.

1982 ◽  
Author(s):  
Patrick Joseph McKenna ◽  
Jeff E. Graham ◽  
Wilbur L. Hankey
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Far Field ◽  
Field Boundary ◽  
Navier Stokes Equations

scholarly journals On the far-field boundary condition treatment in the framework of aeromechanical computations using ANSYS CFX

2020 ◽  
pp. 095765092096269
Author(s):  
Tobias R Mueller ◽  
Damian M Vogt ◽  
Magnus Fischer ◽  
Bent A Phillipsen
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Unsteady Aerodynamics ◽  
Navier Stokes ◽  
Test Case ◽  
Far Field ◽  
Field Boundary ◽  
Navier Stokes Equations ◽  
Ansys Cfx

This numerical study aims at predicting the reflective behavior of different conventional inlet and outlet far-field boundary conditions as well as available non-reflecting boundary conditions (NRBC) implemented in the commercial CFD solver ANSYS CFX. An isolated rotor model of an axial turbine stage with prescribed blade displacement is applied as test case to consider a representative application case, while at the same time provoke an unsteady flow field featuring pronounced flow perturbations in the far-field. Since the reflective behavior of the implemented boundary conditions was found inadequate in the given application case, a zonal treatment of the inlet and outlet far-field, based on a modification of the governing Navier-Stokes equations, is investigated. The applied approach has proven its capability to suppress spurious reflections reliably, while at the same time ensures a preservation of the reference flow conditions within the required domain extensions. The results of a case study considering calculation domains of different spatial extent and different treatments of their respective far-fields suggest variations in the steady flow aerodynamics to be of moderate influence on the predicted aerodynamic damping, while spurious reflections were found to falsify the unsteady aerodynamics considerably.

scholarly journals Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Rong An ◽  
Xian Wang
Keyword(s):  
Boundary Conditions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Newton Iteration ◽  
Navier Stokes ◽  
Discretization Method ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element Method ◽  
The Stability

We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.

New boundary conditions in the transition régime

1968 ◽  
Vol 2 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Carlo Cercignani ◽  
Gino Tironi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Navier Stokes ◽  
Main Body ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Flow Heat

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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